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is
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ims
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c
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s
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e
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p
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lv
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g
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An
c
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o
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th
re
e
-
d
ime
n
sio
n
a
l
re
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e
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h
e
o
ry
i
n
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ro
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g
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stra
t
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sa
m
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n
g
a
n
d
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rp
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m
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li
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d
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term
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e
th
e
re
sp
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n
d
e
n
ts
o
f
th
e
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d
y
c
o
m
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th
e
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larg
e
-
c
a
teg
o
rize
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se
n
i
o
r
h
ig
h
sc
h
o
o
ls
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n
Da
v
a
o
Cit
y
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p
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s
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3
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4
.
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istere
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terv
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n
d
c
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te
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ted
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x
p
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rts.
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e
q
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a
n
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it
a
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d
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g
s,
t
h
ro
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g
h
t
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e
m
u
lt
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p
le
re
g
re
ss
io
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tes
t,
re
v
e
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led
th
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t
p
ro
b
lem
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so
lv
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n
g
sk
il
ls
(P
S
S
)
,
g
ro
wt
h
m
in
d
se
t
(G
M
)
,
a
n
d
tea
c
h
e
r
sc
a
ffo
ld
in
g
s
(TS
)
sig
n
ifi
c
a
n
tl
y
p
re
d
ict
stu
d
e
n
ts’
re
sili
e
n
c
y
in
m
a
th
e
m
a
ti
c
s.
F
o
r
t
h
e
q
u
a
li
tativ
e
d
a
ta,
f
o
ll
o
wi
n
g
C
o
laiz
z
i’s
d
a
ta
a
n
a
ly
sis,
t
h
e
fo
ll
o
wi
n
g
th
e
m
e
s
su
rfa
c
e
d
:
i
)
GM
a
n
d
p
o
s
it
iv
e
lea
rn
i
n
g
a
tt
it
u
d
e
s
;
ii
)
a
c
ti
v
e
p
ro
b
lem
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so
lv
i
n
g
stra
teg
ies
;
a
n
d
i
ii
)
s
u
p
p
o
rti
v
e
lea
rn
i
n
g
e
n
v
iro
n
m
e
n
t
(
S
LE
)
a
n
d
TS
.
Th
e
re
su
lt
s
c
o
n
firme
d
t
h
a
t
c
o
g
n
i
ti
v
e
,
p
sy
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h
o
l
o
g
ica
l,
a
n
d
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ial
f
a
c
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re
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n
ifi
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n
t
ly
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late
d
t
o
st
u
d
e
n
ts
’
r
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sili
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n
c
y
i
n
s
o
lv
i
n
g
m
a
th
e
m
a
ti
c
s
p
ro
b
lem
s
a
n
d
th
a
t
d
e
v
e
lo
p
in
g
a
g
ro
wt
h
a
tt
it
u
d
e
,
f
o
ste
rin
g
a
S
LE
,
a
n
d
p
ro
v
id
i
n
g
a
p
p
ro
p
riate
TS
,
c
a
n
h
e
l
p
b
u
il
d
st
u
d
e
n
ts’
m
a
th
e
m
a
ti
c
a
l
re
sili
e
n
c
e
a
n
d
P
S
S
.
K
ey
w
o
r
d
s
:
E
x
p
lan
ato
r
y
s
eq
u
en
tial
Gr
o
wth
m
in
d
s
et
Ma
th
em
atics r
esil
ien
cy
Pro
b
lem
-
s
o
lv
in
g
T
ea
ch
er
s
ca
f
f
o
ld
i
n
g
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
R
o
ar
A.
C
allam
an
C
o
lleg
e
o
f
E
d
u
ca
tio
n
,
Un
iv
e
r
s
ity
o
f
So
u
th
ea
s
ter
n
Ph
ilip
p
in
e
s
I
n
ig
o
St.,
B
o
.
Ob
r
er
o
,
Dav
ao
C
ity
,
Ph
ilip
p
in
es
E
m
ail:
r
ac
allam
an
@
u
s
ep
.
ed
u
.
p
h
1.
I
NT
RO
D
UCT
I
O
N
Pro
b
lem
s
o
lv
in
g
is
co
n
s
id
er
e
d
an
im
p
o
r
tan
t
2
1
s
t
-
ce
n
t
u
r
y
s
k
ill.
As
a
m
atter
o
f
f
ac
t,
o
n
e
o
f
th
e
f
u
n
d
am
e
n
tal
ab
ilit
ies
r
eq
u
ir
ed
b
y
all
p
eo
p
le
to
h
a
n
d
le
th
e
ev
er
-
m
o
r
e
c
o
m
p
licated
d
e
m
an
d
s
o
f
life
is
th
e
ca
p
ac
ity
f
o
r
p
r
o
b
lem
-
s
o
lv
in
g
[
1
]
.
Hen
ce
,
th
e
n
ee
d
f
o
r
s
tu
d
e
n
ts
to
b
e
tau
g
h
t
with
p
r
o
b
lem
-
s
o
lv
in
g
tech
n
iq
u
es
s
in
ce
th
ey
h
elp
th
em
b
ec
o
m
e
m
o
r
e
in
d
e
p
en
d
en
t
a
n
d
d
ev
el
o
p
h
ig
h
er
-
o
r
d
er
t
h
in
k
in
g
s
k
i
ll
s
[
2
]
.
Sp
ec
if
ically
,
it
ass
ess
e
s
p
er
tin
en
t
d
ata,
t
h
e
p
r
o
b
lem
’
s
lin
k
to
it,
an
d
t
h
e
p
r
o
b
lem
its
elf
u
s
in
g
p
r
o
b
lem
-
s
o
lv
in
g
tech
n
iq
u
es.
Ho
wev
er
,
th
e
f
ac
t
is
th
at
th
er
e
ar
e
s
till
m
an
y
s
tu
d
en
ts
wh
o
h
av
e
d
if
f
icu
lty
i
n
im
p
r
o
v
in
g
th
eir
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
(
PS
S)
[
3
]
an
d
alth
o
u
g
h
p
r
o
b
lem
s
o
lv
in
g
s
k
ill
is
n
o
t
n
ew,
u
n
til
n
o
w
s
ev
er
al
f
ac
to
r
s
p
o
s
e
a
h
ig
h
er
r
is
k
o
f
d
ec
r
ea
s
in
g
m
ath
e
m
atics
lear
n
in
g
ac
h
iev
e
m
en
t
wh
ich
b
ec
o
m
es
a
ch
allen
g
e
as
well
as
cr
ea
tes
v
ar
io
u
s
an
x
iety
f
o
r
s
tu
d
e
n
ts
.
Desp
ite
th
is
,
th
e
lear
n
in
g
p
r
o
ce
s
s
ca
n
s
till
b
e
co
n
tr
o
lled
if
s
tu
d
en
ts
h
av
e
th
e
ab
ilit
y
to
s
u
r
v
iv
e
th
r
o
u
g
h
a
p
o
s
itiv
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attitu
d
e
as a
f
o
r
m
o
f
ad
a
p
tatio
n
f
r
o
m
a
b
n
o
r
m
al
s
itu
atio
n
s
.
Seen
f
r
o
m
a
p
o
in
t
o
f
v
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n
ter
ed
o
n
h
u
m
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p
s
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o
lo
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th
er
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ar
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m
a
n
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ef
in
itio
n
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o
f
r
esil
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th
at
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k
at
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b
j
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p
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as
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v
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co
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ce
p
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tr
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d
u
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o
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wid
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ac
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p
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n
ee
d
to
clar
if
y
an
d
d
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f
in
e
its
co
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s
tr
u
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I
n
th
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co
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tex
t
o
f
th
is
s
tu
d
y
,
m
ath
em
atica
l
r
esil
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s
h
o
wn
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r
o
m
a
p
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f
ea
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in
f
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allen
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a
n
d
d
if
f
ic
u
lties
in
lear
n
in
g
m
ath
em
atics.
T
h
ese
p
o
s
itiv
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
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&
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N:
2252
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8
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B
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th
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co
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a
s
eq
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tia
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p
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ed
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s
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d
en
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ilien
ce
in
…
(
R
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r
A
.
C
a
lla
ma
n
)
1377
attitu
d
es
in
clu
d
e
h
ar
d
w
o
r
k
a
n
d
g
o
o
d
lan
g
u
ag
e
s
k
ills
,
s
elf
-
co
n
f
id
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ce
,
as
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ein
g
d
ilig
en
t
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d
to
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ab
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k
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lab
o
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ativ
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with
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s
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av
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u
a
g
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s
k
ills
to
ex
p
r
ess
m
ath
em
atica
l u
n
d
er
s
tan
d
in
g
,
an
d
m
aster
m
ath
em
atic
s
lear
n
in
g
th
eo
r
y
[
4
]
.
Fu
r
th
er
m
o
r
e
,
m
ath
em
atica
l
r
e
s
ilien
ce
ac
k
n
o
wled
g
es
s
o
cial
an
d
em
o
tio
n
al
r
esp
o
n
s
es
to
t
h
e
s
u
b
ject
th
at
n
ee
d
to
b
e
an
ticip
ated
an
d
m
an
ag
e
d
to
s
u
p
p
o
r
t
en
j
o
y
m
en
t
an
d
s
u
cc
ess
.
T
h
er
e
ar
e
f
o
u
r
k
e
y
asp
ec
ts
in
b
u
ild
in
g
m
ath
em
atica
l r
esil
ien
ce
:
i)
h
a
v
in
g
a
g
r
o
wth
m
in
d
s
et
(
GM
)
;
ii)
b
eliev
in
g
th
at
m
ath
em
atica
l
ca
p
ab
ilit
y
ca
n
im
p
r
o
v
e
th
r
o
u
g
h
ef
f
o
r
t
with
ef
f
ec
tiv
e
s
tr
ateg
ies;
ii
i)
k
n
o
win
g
th
at
m
ath
ca
n
h
av
e
p
e
r
s
o
n
al
v
alu
e,
is
o
f
v
alu
e
in
th
e
wo
r
ld
an
d
th
at
th
e
lear
n
er
is
v
alu
ed
as a
m
ath
em
atician
(
e.
g
.
in
th
eir
class
)
,
k
n
o
win
g
th
at
lear
n
in
g
m
ath
ca
n
in
v
o
l
v
e
s
tr
u
g
g
le
a
n
d
‘
g
ettin
g
s
tu
ck
’
a
n
d
t
h
at
t
h
is
is
to
b
e
ex
p
ec
ted
r
ath
e
r
th
an
a
v
o
id
e
d
;
an
d
iv
)
k
n
o
win
g
h
o
w
to
f
in
d
an
d
e
n
lis
t
s
u
p
p
o
r
t to
s
tay
in
t
h
e
‘
g
r
o
wth
zo
n
e’
[
5
]
.
Giv
en
th
e
d
if
f
e
r
en
t
d
ef
in
itio
n
s
o
f
m
at
h
em
atics
r
esil
ien
cy
,
i
t
is
q
u
ite
i
n
ter
esti
n
g
o
n
t
h
e
p
ar
t
o
f
th
e
r
esear
ch
er
to
s
tu
d
y
th
e
in
t
r
icate
in
ter
p
lay
o
f
co
g
n
itiv
e,
p
s
y
ch
o
lo
g
ical,
an
d
s
o
cial
f
ac
to
r
s
th
at
s
ig
n
if
ican
tly
s
h
ap
es
an
in
d
iv
id
u
al
’
s
m
ath
e
m
atics
r
esil
ien
cy
in
p
r
o
b
lem
-
s
o
lv
in
g
.
M
o
r
eo
v
e
r
,
t
h
e
r
esear
ch
er
b
eliev
es
th
at
u
n
d
er
s
tan
d
i
n
g
an
d
ad
d
r
ess
in
g
th
ese
m
u
ltifa
ce
ted
in
f
lu
en
ce
s
ca
n
f
o
s
ter
a
r
esil
ien
t
an
d
ad
ap
tiv
e
ap
p
r
o
ac
h
to
m
ath
em
atica
l
p
r
o
b
lem
-
s
o
lv
i
n
g
th
at
u
ltima
tely
en
h
an
ce
s
th
e
in
d
iv
id
u
als
’
ca
p
ac
ity
to
n
a
v
ig
a
te
an
d
co
n
q
u
e
r
th
e
co
m
p
lex
ities
o
f
m
ath
e
m
atica
l ta
s
k
s
.
Un
lik
e
tr
ad
itio
n
al
r
esil
ien
ce
th
eo
r
ies
th
at
f
o
cu
s
p
r
im
ar
ily
o
n
in
d
iv
id
u
al
g
r
it,
th
e
th
r
ee
-
d
i
m
en
s
io
n
al
r
esil
ien
cy
th
eo
r
y
[
6
]
p
o
s
its
th
at
m
ath
em
atica
l
s
u
cc
ess
s
tem
s
f
r
o
m
th
e
s
y
n
er
g
y
o
f
co
g
n
itiv
e,
p
s
y
c
h
o
lo
g
ical,
an
d
s
o
cial
f
ac
to
r
s
.
T
h
is
s
tu
d
y
v
alid
ates
th
e
s
ec
o
n
d
p
r
o
p
o
s
it
io
n
o
f
th
e
t
h
eo
r
y
wh
ich
s
tates
th
at
th
e
co
g
n
itiv
e,
p
s
y
ch
o
lo
g
ical
an
d
s
o
cial
f
ac
t
o
r
s
ar
e
i
n
f
lu
en
tial
t
o
a
s
tu
d
en
ts
’
r
esil
ien
cy
in
s
o
lv
i
n
g
m
ath
em
a
tical
p
r
o
b
le
m
s
.
I
t
also
d
eter
m
in
es
t
h
e
v
alid
it
y
o
f
th
e
t
h
ir
d
p
r
o
p
o
s
itio
n
s
ta
tin
g
th
at
d
ev
elo
p
i
n
g
a
g
r
o
wth
attitu
d
e,
f
o
s
ter
in
g
a
s
u
p
p
o
r
tiv
e
lear
n
in
g
en
v
ir
o
n
m
en
t
(
SLE
)
,
an
d
p
r
o
v
id
i
n
g
a
p
p
r
o
p
r
iate
teac
h
er
s
ca
f
f
o
ld
in
g
(
T
S)
ca
n
h
elp
b
u
ild
m
ath
em
atica
l
r
esil
ien
ce
an
d
p
r
o
b
lem
-
s
o
lv
in
g
p
r
o
ce
s
s
.
Fu
r
th
er
m
o
r
e,
th
is
r
esear
ch
s
ee
k
s
to
d
eter
m
in
e
th
e
co
g
n
itiv
e,
p
s
y
ch
o
lo
g
ical,
an
d
s
o
cial
f
ac
to
r
s
th
at
in
f
lu
en
ce
d
s
tu
d
en
ts
’
m
ath
em
atics
r
esil
ien
ce
;
an
d
g
ain
d
ee
p
er
in
s
ig
h
ts
in
to
th
e
liv
ed
ex
p
e
r
ie
n
ce
s
an
d
p
e
r
s
p
ec
tiv
es
o
f
s
tu
d
e
n
ts
with
v
ar
y
in
g
lev
els
o
f
r
esil
ien
ce
,
f
o
cu
s
in
g
o
n
th
eir
co
g
n
itiv
e
p
r
o
ce
s
s
es,
em
o
tio
n
al
r
esp
o
n
s
es,
an
d
s
o
cial
in
t
er
ac
tio
n
s
d
u
r
in
g
p
r
o
b
lem
-
s
o
l
v
in
g
ac
tiv
ities
.
2.
M
E
T
H
O
D
T
h
is
s
tu
d
y
u
tili
ze
d
an
e
x
p
la
n
ato
r
y
s
eq
u
en
tial
m
ix
e
d
-
m
et
h
o
d
s
d
esig
n
.
I
n
th
is
d
esig
n
,
r
esear
ch
er
s
ty
p
ically
co
n
n
ec
t
th
e
two
p
h
a
s
es
b
y
s
elec
tin
g
q
u
alitativ
e
p
ar
ticip
an
ts
b
ased
o
n
th
e
q
u
an
t
itativ
e
r
esu
lts
f
r
o
m
th
e
f
ir
s
t
p
h
ase
[
7
]
.
Sp
ec
if
ically
,
th
e
s
tu
d
y
ap
p
lied
th
e
f
o
llo
w
-
u
p
ex
p
lan
atio
n
m
o
d
el,
wh
e
r
ein
th
e
r
esear
ch
er
s
o
u
g
h
t
to
c
lar
if
y
a
n
d
e
n
r
ich
th
e
q
u
an
titativ
e
f
in
d
in
g
s
th
r
o
u
g
h
q
u
alitativ
e
d
ata.
T
h
e
q
u
alita
tiv
e
d
ata
wer
e
u
s
ed
to
in
ter
p
r
et
an
d
e
x
p
lain
t
h
e
r
esu
lts
o
b
tain
ed
f
r
o
m
t
h
e
q
u
an
titativ
e
an
aly
s
is
.
T
h
e
q
u
an
titativ
e
co
m
p
o
n
e
n
t
em
p
lo
y
ed
a
d
escr
ip
tiv
e
-
co
r
r
elatio
n
al
ap
p
r
o
ac
h
,
wh
i
le
th
e
q
u
alitativ
e
p
ar
t
u
s
ed
a
d
escr
ip
tiv
e
p
h
en
o
m
en
o
lo
g
ical
ap
p
r
o
ac
h
.
T
h
is
d
esig
n
was
ap
p
r
o
p
r
ia
te
b
ec
au
s
e
th
e
s
tu
d
y
aim
e
d
to
d
eter
m
in
e
th
e
s
ig
n
if
ican
t
co
g
n
itiv
e,
p
s
y
ch
o
lo
g
ical,
an
d
s
o
cial
f
ac
t
o
r
s
i
n
f
lu
en
cin
g
s
tu
d
e
n
ts
’
m
ath
em
atics
r
esil
ien
cy
b
y
ad
m
in
is
ter
in
g
a
s
u
r
v
ey
q
u
esti
o
n
n
air
e
to
th
e
r
esp
o
n
d
en
ts
,
f
o
llo
wed
b
y
an
in
-
d
e
p
th
in
ter
v
iew
to
s
u
p
p
o
r
t
an
d
co
n
tex
tu
alize
th
e
q
u
an
titativ
e
r
esu
lts
.
T
h
e
s
tu
d
y
was
co
n
d
u
cted
in
s
ix
lar
g
e
p
u
b
lic
s
en
io
r
h
ig
h
s
ch
o
o
ls
(
SHS)
in
Dav
ao
C
ity
d
u
r
in
g
s
ch
o
o
l
y
ea
r
(
SY)
2
0
2
3
–
2
0
2
4
.
T
h
e
s
e
s
ch
o
o
ls
h
av
e
th
e
h
i
g
h
est
n
u
m
b
er
o
f
en
r
o
llees
in
th
e
d
iv
is
io
n
an
d
ar
e
lo
ca
ted
ac
r
o
s
s
th
e
city
’
s
th
r
ee
c
o
n
g
r
ess
io
n
al
d
is
tr
icts
,
en
s
u
r
in
g
g
eo
g
r
a
p
h
ical
d
iv
e
r
s
ity
in
th
e
s
am
p
le.
Fo
r
th
e
q
u
an
titativ
e
d
ata,
th
e
r
esp
o
n
d
en
ts
wer
e
5
7
9
n
o
n
-
s
cien
ce
,
te
ch
n
o
lo
g
y
,
en
g
i
n
ee
r
in
g
,
an
d
m
ath
em
atics
(
STE
M
)
SHS
s
tu
d
en
ts
en
r
o
lled
in
th
e
s
ec
o
n
d
s
em
ester
.
T
h
e
s
am
p
le
co
n
s
is
ted
o
f
2
4
4
m
ales
(
4
2
.
1
4
%)
an
d
3
3
5
f
em
ales
(
5
7
.
8
6
%).
Acc
o
r
d
i
n
g
to
C
o
m
r
ey
an
d
L
ee
[
8
]
,
a
m
i
n
im
u
m
o
f
5
0
0
o
b
s
er
v
atio
n
s
is
id
ea
l
i
n
f
ac
to
r
an
aly
s
is
to
estab
lis
h
v
ali
d
ity
,
r
eliab
ilit
y
,
an
d
to
s
u
p
p
o
r
t
m
u
ltip
le
lin
ea
r
r
eg
r
ess
io
n
.
Stra
tifie
d
s
am
p
lin
g
was
u
s
ed
to
d
eter
m
in
e
th
e
n
u
m
b
er
o
f
r
e
s
p
o
n
d
en
ts
,
as
r
ec
o
m
m
e
n
d
ed
b
y
C
r
eswell
[
9
]
,
wh
ic
h
in
v
o
lv
es
d
iv
i
d
in
g
t
h
e
p
o
p
u
latio
n
in
to
h
o
m
o
g
en
eo
u
s
s
tr
ata
b
ased
o
n
ce
r
tain
ch
ar
ac
ter
is
ti
cs.
T
wo
n
o
n
-
STE
M
clas
s
es
p
er
s
ch
o
o
l
wer
e
r
an
d
o
m
l
y
s
elec
ted
,
r
esu
ltin
g
i
n
a
to
tal
o
f
1
2
class
es a
n
d
5
7
9
s
tu
d
en
t r
esp
o
n
d
en
ts
.
Fo
r
th
e
q
u
alitativ
e
p
h
ase,
10
p
ar
ticip
an
ts
wer
e
s
elec
ted
f
r
o
m
th
e
s
u
r
v
ey
to
tak
e
p
a
r
t
in
f
o
llo
w
-
up
in
ter
v
iews:
s
ix
wh
o
d
em
o
n
s
tr
ated
h
ig
h
lev
els
o
f
r
esil
ien
ce
an
d
f
o
u
r
wh
o
s
co
r
e
d
lo
w.
All
p
ar
ticip
an
ts
v
o
lu
n
teer
e
d
to
s
h
ar
e
t
h
eir
p
e
r
s
o
n
al
ex
p
er
ie
n
ce
s
an
d
p
er
s
p
ec
tiv
es.
T
h
ey
wer
e
id
e
n
tifie
d
th
r
o
u
g
h
p
u
r
p
o
s
iv
e
s
am
p
lin
g
,
wh
ich
is
ap
p
r
o
p
r
i
ate
wh
en
th
e
r
esear
c
h
er
d
ete
r
m
in
es
wh
at
in
f
o
r
m
atio
n
is
n
ee
d
ed
a
n
d
s
elec
ts
in
d
iv
id
u
als ca
p
ab
le
a
n
d
willin
g
to
p
r
o
v
id
e
it
[
1
0
]
,
[
1
1
]
.
A
r
esear
ch
er
-
m
a
d
e
q
u
esti
o
n
n
air
e
was
u
s
ed
f
o
r
th
e
q
u
an
ti
tativ
e
p
h
ase.
T
h
e
4
-
po
in
t
L
i
k
er
t
s
ca
le
q
u
esti
o
n
n
air
e
was
v
alid
ated
b
y
a
p
s
y
ch
o
m
etr
ician
o
r
p
s
y
ch
o
lo
g
is
t,
a
la
n
g
u
a
g
e
ex
p
er
t,
an
d
a
m
ath
em
atics
ed
u
ca
tio
n
e
x
p
er
t
.
A
co
n
f
ir
m
at
o
r
y
f
ac
t
o
r
a
n
aly
s
is
(
C
FA)
was
co
n
d
u
cted
to
ex
am
in
e
wh
eth
e
r
th
e
q
u
esti
o
n
n
air
e
item
s
alig
n
ed
with
th
e
laten
t
co
n
s
tr
u
ct
o
f
m
ath
e
m
atics
r
esil
i
en
ce
[
1
2
]
.
R
esu
lts
r
ev
ea
led
s
e
v
en
co
n
s
tr
u
cts
with
th
eir
co
r
r
esp
o
n
d
i
n
g
c
o
m
p
o
s
it
e
r
eliab
ilit
y
(
C
R
)
:
7
item
s
f
o
r
PSS
(
C
R
=0
.
7
7
2
)
;
4
item
s
f
o
r
GM
(
C
R
=0
.
7
6
0
)
;
9
item
s
f
o
r
life
lo
n
g
lear
n
in
g
en
g
ag
em
en
t
(
L
L
E
)
(
0
.
8
2
1
)
;
9
item
s
f
o
r
cr
i
tical
th
in
k
in
g
s
k
ills
(
C
T
S)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
2
,
Ap
r
il
20
26
:
1
3
7
6
-
1
3
8
7
1378
(
C
R
=0
.
7
9
9
)
;
1
0
item
s
f
o
r
m
ath
an
x
iety
(
MA
)
(
C
R
=0
.
8
5
8
)
;
1
0
item
s
f
o
r
SLE
(
0
.
8
9
6
)
;
an
d
9
item
s
f
o
r
teac
h
in
g
s
ca
f
f
o
l
d
in
g
(
0
.
8
9
1
)
.
Me
an
wh
ile,
th
e
in
ter
v
iew
g
u
i
d
e
f
o
r
th
e
q
u
alitativ
e
p
h
ase
was
cr
af
ted
af
ter
th
e
q
u
an
titativ
e
an
aly
s
is
an
d
v
al
id
ated
b
y
two
q
u
alitativ
e
r
esear
ch
ex
p
er
ts
.
I
t
co
n
s
is
ted
o
f
10
o
p
en
-
e
n
d
ed
q
u
esti
o
n
s
d
esig
n
ed
to
elicit
s
tu
d
en
ts
’
ex
p
er
ie
n
ce
s
in
m
ath
em
atic
al
p
r
o
b
lem
s
o
lv
in
g
.
T
o
g
ath
er
d
ata,
th
e
r
esear
ch
er
f
ir
s
t
s
o
u
g
h
t
p
er
m
is
s
io
n
f
r
o
m
th
e
s
ch
o
o
ls
d
iv
is
io
n
s
u
p
er
in
ten
d
en
t
an
d
s
ch
o
o
l
p
r
in
cip
als,
as
well
as
ap
p
r
o
v
al
f
r
o
m
t
h
e
eth
ics
r
esear
ch
co
m
m
ittee.
T
h
e
5
7
9
SHS
r
esp
o
n
d
en
ts
wer
e
id
en
tifie
d
th
r
o
u
g
h
s
tr
ati
f
ied
r
an
d
o
m
s
am
p
lin
g
,
with
two
s
ec
tio
n
s
p
er
s
ch
o
o
l
r
an
d
o
m
ly
ch
o
s
en
.
T
h
e
q
u
esti
o
n
n
air
e
an
d
in
te
r
v
iew
g
u
id
e
wer
e
v
alid
ated
b
y
f
iv
e
e
x
p
er
ts
wh
o
s
e
f
ee
d
b
ac
k
in
f
o
r
m
ed
th
e
f
in
al
v
er
s
io
n
o
f
th
e
in
s
tr
u
m
en
ts
.
T
h
e
q
u
e
s
tio
n
n
air
e
was
ad
m
in
is
ter
ed
v
ia
Go
o
g
le
Fo
r
m
s
,
an
d
s
tu
d
en
ts
wer
e
g
iv
en
15
–
3
0
m
i
n
u
tes
to
r
esp
o
n
d
.
I
n
t
er
v
iews
wer
e
co
n
d
u
cte
d
af
te
r
an
aly
zin
g
th
e
q
u
an
titativ
e
r
esu
lts
.
T
h
e
c
o
llected
d
ata
wer
e
th
en
s
o
r
ted
,
ta
b
u
la
ted
,
an
d
s
u
b
jecte
d
t
o
s
tatis
tic
al
an
aly
s
is
,
wh
ile
th
e
r
ec
o
r
d
e
d
in
ter
v
iews
wer
e
tr
an
s
cr
ib
ed
an
d
an
aly
ze
d
th
em
atica
lly
.
Hy
p
o
th
eses
wer
e
test
ed
at
th
e
0
.
0
5
lev
el
o
f
s
ig
n
if
ic
an
ce
.
Mu
ltip
le
r
eg
r
ess
io
n
an
aly
s
is
was
em
p
lo
y
ed
to
d
eter
m
i
n
e
th
e
in
f
lu
en
ce
o
f
th
e
in
d
ep
en
d
e
n
t
v
ar
iab
les
—
C
T
S
,
P
SS
,
GM
,
MA
,
LLE
,
SLE
,
an
d
T
S
—
o
n
th
e
d
ep
en
d
en
t
v
ar
ia
b
le,
m
ath
em
atics
r
esil
ien
cy
in
p
r
o
b
lem
s
o
lv
in
g
.
A
two
-
taile
d
test
at
th
e
0
.
0
5
lev
el
o
f
s
i
g
n
if
ican
ce
was
ap
p
lied
.
Fo
r
t
h
e
q
u
alitativ
e
d
ata,
C
o
laizz
i’
s
s
ev
en
-
s
tep
th
em
atic
an
aly
s
is
wa
s
u
s
ed
.
T
h
is
in
v
o
lv
ed
r
ep
ea
ted
l
y
r
ea
d
in
g
th
e
i
n
ter
v
iew
r
esp
o
n
s
es,
ex
tr
ac
tin
g
s
ig
n
if
ican
t
s
tatem
en
ts
,
f
o
r
m
u
latin
g
m
ea
n
in
g
s
,
cl
u
s
ter
in
g
s
im
ilar
m
ea
n
in
g
s
in
t
o
th
em
es,
p
r
o
d
u
cin
g
an
ex
h
au
s
tiv
e
d
escr
ip
tio
n
o
f
th
e
p
h
en
o
m
en
o
n
,
id
en
tify
i
n
g
its
f
u
n
d
am
e
n
tal
s
tr
u
ctu
r
e,
an
d
r
etu
r
n
in
g
th
e
s
y
n
th
esized
f
in
d
in
g
s
to
th
e
p
a
r
ticip
an
ts
f
o
r
v
alid
atio
n
.
Prio
r
to
d
ata
co
llectio
n
,
th
e
r
esear
ch
er
s
o
b
tain
ed
eth
ics
clea
r
an
ce
f
r
o
m
th
e
C
eb
u
No
r
m
al
Un
iv
er
s
ity
’
s
R
esear
ch
E
th
ics
C
o
m
m
ittee
-
C
NU
E
R
C
C
o
d
e
-
8
9
6
/2
0
2
4
-
0
2
.
T
h
e
m
ain
r
esear
ch
er
b
r
ief
e
d
th
e
s
tu
d
en
t
-
r
esp
o
n
d
en
ts
o
n
th
e
s
tu
d
y
’
s
p
u
r
p
o
s
e
a
n
d
b
e
n
ef
its
.
T
h
o
s
e
wh
o
co
n
s
en
ted
wer
e
p
r
o
v
id
ed
with
in
f
o
r
m
e
d
co
n
s
en
t o
r
ass
en
t f
o
r
m
s
an
d
w
er
e
ask
ed
to
s
ig
n
a
n
d
d
ate
th
e
m
to
co
n
f
ir
m
th
eir
v
o
lu
n
tar
y
p
ar
ticip
atio
n
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Qu
an
titativ
e
f
in
d
i
n
g
s
ar
e
f
ir
s
t
r
ep
o
r
ted
to
id
en
tif
y
th
e
s
ig
n
if
i
ca
n
t
co
g
n
itiv
e,
p
s
y
ch
o
l
o
g
ical,
an
d
s
o
cial
f
ac
to
r
s
th
at
i
n
f
lu
en
ce
s
tu
d
en
ts
’
m
ath
em
atics
r
esil
ien
cy
.
T
h
es
e
r
esu
lts
th
en
g
u
id
e
d
t
h
e
q
u
alitativ
e
p
h
ase,
w
h
er
e
s
tu
d
en
ts
’
ex
p
er
ien
ce
s
wer
e
e
x
p
lo
r
ed
to
clar
if
y
a
n
d
d
ee
p
en
t
h
e
u
n
d
e
r
s
tan
d
in
g
o
f
th
e
p
atter
n
s
r
ev
ea
led
in
th
e
s
tatis
t
ical
an
aly
s
is
.
T
o
g
eth
er
,
th
e
in
teg
r
ated
f
i
n
d
in
g
s
p
r
o
v
id
e
a
co
h
er
e
n
t
ex
p
lan
atio
n
o
f
h
o
w
v
ar
i
o
u
s
p
r
ed
icto
r
s
s
h
ap
e
s
tu
d
e
n
ts
’
r
esil
ien
ce
in
m
ath
em
atica
l p
r
o
b
le
m
-
s
o
lv
in
g
task
s
.
3
.
1
.
Q
ua
ntit
a
t
iv
e
f
ind
ing
s
I
n
a
m
u
ltip
le
r
eg
r
ess
io
n
a
n
aly
s
is
s
tu
d
y
,
it
is
v
ital
t
o
en
s
u
r
e
th
at
th
e
ass
u
m
p
tio
n
s
o
f
n
o
m
u
ltico
llin
ea
r
ity
h
av
e
b
ee
n
s
atis
f
ied
.
I
n
s
tatis
tics
,
m
u
ltico
llin
ea
r
ity
ex
is
t
w
h
en
two
o
r
m
o
r
e
p
r
ed
icto
r
v
ar
iab
les
ar
e
h
ig
h
ly
c
o
r
r
elate
d
[
1
3
]
.
As
r
e
f
lecte
d
in
T
ab
l
e
1
,
th
e
Pear
s
o
n
c
o
r
r
elatio
n
s
am
o
n
g
th
e
s
ev
e
n
p
r
ed
ictiv
e
v
ar
ia
b
les
wer
e
ca
lcu
lated
.
I
t
ca
n
b
e
n
o
te
d
th
at
n
o
n
e
o
f
th
e
v
ar
iab
les
h
ad
a
th
r
e
s
h
o
ld
o
f
0
.
8
0
.
T
h
is
r
esu
lt
s
h
o
ws
th
at
n
o
two
v
ar
iab
les
ar
e
clo
s
ely
r
elate
d
to
ea
c
h
o
th
er
.
T
h
u
s
,
th
e
ass
u
m
p
tio
n
o
f
n
o
m
u
ltico
llin
ea
r
ity
h
as b
ee
n
s
atis
f
ied
.
T
ab
le
1
.
C
o
r
r
elatio
n
am
o
n
g
th
e
p
r
ed
icto
r
v
ar
iab
les
V
a
r
i
a
b
l
e
s
C
TS
PSS
GM
MA
LLE
S
LE
TS
C
TS
0
.
7
4
3
0
.
4
1
4
-
0
.
0
9
3
0
.
5
9
5
0
.
5
4
9
0
.
5
2
8
PSS
0
.
7
4
3
0
.
4
7
1
-
0
.
0
6
9
0
.
5
4
5
0
.
5
7
5
0
.
5
2
6
GM
0
.
4
7
1
0
.
4
1
4
0
.
0
2
1
0
.
5
6
0
0
.
5
2
1
0
.
5
3
5
MA
-
0
.
0
9
3
-
0
.
0
6
9
0
.
0
2
1
0
.
1
1
1
0
.
0
9
8
0
.
1
3
4
LLE
0
.
5
9
5
0
.
5
4
5
0
.
5
6
0
0
.
1
1
1
0
.
5
9
8
0
.
5
4
0
S
LE
0
.
5
4
9
0
.
5
7
5
0
.
5
2
1
0
.
0
9
8
0
.
5
9
8
0
.
7
7
0
TS
0
.
5
2
8
0
.
5
2
6
0
.
5
3
5
0
.
1
3
4
0
.
5
4
0
0
.
7
7
0
I
n
T
a
b
le
2
,
th
e
esti
m
ate
f
o
r
e
ac
h
p
r
ed
icto
r
v
ar
iab
le
r
ep
r
esen
ts
th
e
ex
p
ec
ted
ch
an
g
e
in
m
ath
em
atics
r
esil
ien
cy
ass
o
ciate
d
with
a
o
n
e
-
u
n
it
i
n
cr
ea
s
e
in
t
h
at
v
ar
ia
b
le,
wh
ile
h
o
ld
in
g
all
o
th
er
v
ar
i
ab
les
co
n
s
tan
t.
T
h
i
s
v
alu
e
q
u
an
tifie
s
th
e
d
ir
ec
tio
n
an
d
s
tr
en
g
th
o
f
th
e
r
elatio
n
s
h
i
p
.
A
p
o
s
itiv
e
esti
m
ate
s
ig
n
if
ies
th
at
h
ig
h
er
v
alu
es
o
f
th
e
p
r
e
d
icto
r
v
ar
ia
b
le
ar
e
ass
o
ciate
d
with
g
r
ea
ter
m
ath
em
atics
r
esil
ien
cy
,
an
d
v
ice
v
er
s
a
f
o
r
a
n
eg
ativ
e
esti
m
ate.
Me
an
wh
ile,
th
e
s
tan
d
ar
d
er
r
o
r
(
SE)
r
e
f
lects
th
e
p
r
ec
is
io
n
o
f
th
e
esti
m
ated
co
ef
f
icien
t.
Sm
aller
SE
v
alu
es
in
d
icate
m
o
r
e
p
r
ec
is
e
esti
m
ates,
wh
ile
lar
g
er
SEs
s
u
g
g
est
g
r
ea
te
r
u
n
ce
r
tain
ty
.
I
t
h
elp
s
u
s
g
au
g
e
th
e
co
n
f
id
en
ce
in
ter
v
al
a
r
o
u
n
d
th
e
esti
m
ated
ef
f
ec
t size.
T
h
e
t
-
s
tatis
tic
in
d
icate
s
h
o
w
m
an
y
SE
t
h
e
co
e
f
f
icien
t
esti
m
ate
is
awa
y
f
r
o
m
ze
r
o
.
I
t
is
u
s
ed
to
ass
ess
th
e
s
tatis
tical
s
ig
n
if
ican
ce
o
f
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
p
r
ed
icto
r
a
n
d
th
e
o
u
tco
m
e
v
a
r
iab
le.
A
s
tatis
tically
Evaluation Warning : The document was created with Spire.PDF for Python.
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th
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p
r
ed
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r
s
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f stu
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…
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1379
s
ig
n
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ican
t
co
ef
f
icien
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(
b
ased
o
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ch
o
s
en
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o
f
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n
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ests
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at
th
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o
b
s
er
v
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ass
o
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is
u
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u
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ch
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ce
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h
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co
r
r
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o
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d
in
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ep
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ts
th
e
p
r
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b
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y
o
f
o
b
s
er
v
in
g
a
t
-
s
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tic
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ex
tr
em
e
as
th
e
o
n
e
ca
lcu
late
d
,
ass
u
m
in
g
n
o
r
ea
l
r
elatio
n
s
h
ip
ex
is
ts
(
n
u
ll
h
y
p
o
th
esis
)
.
Sm
aller
p
-
v
alu
es
p
r
o
v
id
e
s
tr
o
n
g
er
ev
id
e
n
ce
ag
a
in
s
t th
e
n
u
ll h
y
p
o
th
esis
,
in
d
ica
tin
g
a
s
tatis
tically
s
ig
n
if
ican
t a
s
s
o
ciatio
n
.
T
ab
le
2
.
Mu
ltip
le
r
e
g
r
ess
io
n
o
f
m
ath
em
atics r
esil
ien
cy
P
r
e
d
i
c
t
o
r
Est
i
m
a
t
e
SE
T
p
I
n
t
e
r
c
e
p
t
2
.
1
0
7
0
.
1
4
4
1
4
.
6
1
4
0
.
0
0
0
PSS
0
.
1
4
1
0
.
0
5
0
2
.
7
9
8
0
.
0
0
5
C
TS
-
0
.
0
2
5
0
.
0
5
5
-
0
.
4
5
0
.
6
5
3
GM
0
.
0
7
7
0
.
0
3
6
2
.
1
4
1
0
.
0
3
3
LLE
0
.
0
4
8
0
.
0
4
9
0
.
9
8
1
0
.
3
2
7
MA
0
.
0
5
2
0
.
0
2
6
1
.
9
6
0
.
0
5
0
S
LE
-
0
.
0
3
6
0
.
0
5
1
-
0
.
7
0
4
0
.
4
8
2
TS
0
.
1
0
7
0
.
0
5
1
2
.
1
1
6
0
.
0
3
5
T
h
e
r
eg
r
ess
io
n
r
esu
lts
s
h
o
w
th
at
f
o
u
r
o
f
th
e
s
ev
en
in
d
ep
e
n
d
e
n
t
v
ar
iab
les
wh
ich
ar
e,
C
T
S
,
LLE
,
MA
,
an
d
SLE
,
d
o
n
o
t
s
ig
n
if
ican
tly
p
r
ed
ict
s
tu
d
en
ts
’
m
ath
em
atic
s
r
esil
ien
cy
in
p
r
o
b
lem
s
o
lv
in
g
,
as
in
d
icate
d
b
y
th
eir
p
-
v
alu
es
b
ein
g
ab
o
v
e
0
.
0
5
.
T
h
is
m
ea
n
s
th
er
e
i
s
in
s
u
f
f
icien
t
ev
id
en
ce
t
o
co
n
clu
d
e
t
h
at
th
ese
f
ac
to
r
s
ar
e
r
elate
d
to
r
esil
ien
cy
.
I
n
co
n
tr
ast,
th
r
ee
v
a
r
iab
les
wh
ich
a
r
e
PSS
,
GM
,
an
d
TS
ar
e
s
tati
s
tically
s
ig
n
if
ican
t
p
r
ed
icto
r
s
.
Sp
ec
if
ically
,
PSS
s
tr
o
n
g
ly
in
f
lu
en
ce
s
tu
d
e
n
ts
’
m
ath
em
atics
r
esil
ien
ce
,
with
a
r
eg
r
ess
io
n
co
ef
f
icien
t
o
f
0
.
1
4
1
an
d
a
p
-
v
alu
e
o
f
0
.
0
0
5
,
in
d
icatin
g
th
at
h
ig
h
er
PSS
ar
e
ass
o
ciate
d
wit
h
g
r
ea
ter
r
esil
ien
cy
.
Ov
er
all,
th
e
f
in
d
i
n
g
s
h
ig
h
lig
h
t
th
at
co
g
n
itiv
e,
p
s
y
ch
o
lo
g
ical,
an
d
s
o
cial
f
ac
to
r
s
p
lay
a
cr
u
c
ial
r
o
le
in
s
h
ap
in
g
s
tu
d
en
ts
’
r
esil
ien
c
e
in
m
ath
em
atics.
T
h
e
r
esu
lt
is
in
co
n
f
o
r
m
an
ce
i
n
th
e
s
tu
d
y
o
f
Har
s
ela
an
d
Asi
h
[
1
4
]
wh
o
v
iewe
d
th
at
th
e
ac
h
iev
em
en
t
o
f
s
tu
d
en
ts
’
a
b
ilit
y
to
s
o
lv
e
m
ath
em
atica
l
p
r
o
b
le
m
s
af
f
ec
ts
th
eir
r
esil
ien
cy
in
m
ath
em
atics.
Stu
d
en
ts
ar
e
q
u
ite
ca
p
ab
le
o
f
o
v
er
c
o
m
in
g
th
e
d
if
f
icu
lties
th
ey
f
ac
e
wh
e
n
l
ea
r
n
in
g
m
at
h
em
atics.
Ad
d
itio
n
ally
,
th
e
r
esear
ch
in
d
icate
s
th
at
th
er
e
is
a
p
o
s
it
iv
e
an
d
s
ig
n
if
ican
t
r
e
latio
n
s
h
ip
b
etwe
en
m
ath
em
atica
l
r
esil
ien
ce
an
d
s
tu
d
en
t
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
y
,
with
m
ath
em
atica
l r
esil
ien
ce
b
ein
g
u
s
ed
to
p
r
ed
ict
th
e
lev
el
o
f
ac
a
d
em
ic
ab
ilit
y
.
T
h
is
s
u
g
g
ests
th
at
s
tu
d
en
ts
’
ac
h
iev
em
en
t
o
f
m
ath
em
atica
l
p
r
o
b
le
m
-
s
o
lv
in
g
ab
ilit
ies
at
a
m
o
d
er
a
te
lev
el
m
ay
also
b
e
in
f
lu
en
ce
d
b
y
th
eir
lev
el
o
f
m
ath
em
atica
l r
esil
ien
ce
.
T
h
e
s
a
m
e
is
tr
u
e
wi
th
t
h
e
s
tu
d
y
c
o
n
d
u
cte
d
b
y
Ha
r
s
el
a
et
a
l
.
[
1
5
]
w
h
i
c
h
s
h
o
ws
t
h
a
t,
w
h
il
e
t
h
e
e
f
f
ec
t
v
a
r
i
es
d
e
p
e
n
d
i
n
g
o
n
th
e
le
ar
n
e
r
ty
p
e
,
m
at
h
e
m
at
ic
al
r
es
ili
en
ce
a
f
f
ec
ts
s
t
u
d
e
n
ts
’
c
a
p
ac
it
y
t
o
s
o
l
v
e
m
at
h
e
m
a
tic
a
l
ap
p
li
ca
ti
o
n
a
n
d
wo
r
d
p
r
o
b
l
em
s
.
W
h
il
e
i
n
d
e
p
e
n
d
e
n
t
l
ea
r
n
er
s
wit
h
o
n
l
y
m
o
d
er
ate
r
esil
ie
n
c
e
d
i
d
n
o
t
s
i
g
n
if
i
ca
n
t
ly
im
p
r
o
v
e
i
n
t
h
ei
r
a
b
ili
ty
t
o
s
o
l
v
e
w
o
r
d
p
r
o
b
le
m
s
,
th
o
s
e
w
it
h
e
x
c
ell
en
t
r
es
ili
en
ce
we
r
e
b
e
tt
er
a
b
l
e
to
o
v
e
r
c
o
m
e
o
b
s
ta
c
les
.
I
n
a
d
d
iti
o
n
,
t
h
e
a
c
h
iev
em
e
n
t
o
f
m
at
h
e
m
at
ica
l
r
es
ilie
n
c
e,
b
o
t
h
o
v
e
r
al
l
an
d
b
ase
d
o
n
m
at
h
e
m
ati
ca
l
p
r
io
r
k
n
o
wled
g
e,
is
n
o
t
s
ig
n
i
f
ican
tly
af
f
ec
ted
b
y
th
e
ty
p
e
o
f
lear
n
in
g
m
o
d
el
t
h
at
is
u
s
ed
.
Als
o
,
s
tu
d
en
ts
wh
o
r
ec
eiv
e
in
s
tr
u
ctio
n
u
s
in
g
p
r
o
b
lem
-
b
ased
lea
r
n
in
g
m
o
d
els
d
o
n
o
t
s
ig
n
if
ican
tly
o
u
tp
er
f
o
r
m
s
tu
d
e
n
ts
wh
o
r
ec
eiv
e
co
n
v
en
tio
n
al
i
n
s
tr
u
ctio
n
eith
er
o
v
er
all
o
r
b
ased
o
n
p
r
io
r
k
n
o
wled
g
e
i
n
m
ath
em
atic
s
[
1
6
]
.
GM
is
also
f
o
u
n
d
to
b
e
s
tatis
t
ically
s
ig
n
if
ican
t
in
p
r
ed
ictin
g
s
tu
d
en
ts
’
m
at
h
em
atics
r
esil
ien
cy
b
ased
o
n
th
e
r
esu
lts
o
f
t
h
e
m
u
ltip
le
r
eg
r
ess
io
n
an
al
y
s
is
.
T
h
e
f
ac
to
r
h
as
a
n
esti
m
ated
r
eg
r
ess
io
n
co
ef
f
icien
t
o
f
0
.
0
7
7
an
d
a
n
esti
m
ated
SE
0
.
0
3
6
.
T
h
ese
v
alu
es
in
d
icate
th
e
p
r
e
cisi
o
n
o
f
th
e
r
eg
r
ess
io
n
esti
m
ate,
wh
ich
s
u
g
g
ests
th
at
if
th
e
s
tu
d
en
ts
p
o
s
s
ess
a
h
ig
h
lev
el
o
f
GM
,
th
eir
m
ath
e
m
atics
r
esil
ien
cy
in
p
r
o
b
lem
s
o
lv
in
g
will
in
c
r
ea
s
e
an
d
th
at
th
e
esti
m
ated
v
al
u
e
i
s
p
r
ec
is
ely
th
e
tr
u
e
v
alu
e
b
ec
au
s
e
it
is
clo
s
er
to
0
.
O
n
th
e
o
th
er
h
an
d
,
th
e
r
e
is
co
m
p
ellin
g
ev
i
d
en
ce
th
at
th
e
v
ar
iab
le
GM
is
v
er
y
im
p
o
r
ta
n
t
in
m
ath
r
esil
ien
cy
,
as
in
d
icate
d
b
y
th
e
co
m
p
u
ted
t
-
s
tatis
t
ic
v
alu
e
o
f
2
.
1
4
1
an
d
th
e
p
-
v
al
u
e
o
f
0
.
0
3
3
.
I
n
d
ee
d
,
GM
in
te
r
v
en
tio
n
s
h
a
v
e
d
em
o
n
s
tr
ated
en
co
u
r
ag
in
g
b
en
ef
its
in
r
aisi
n
g
s
tu
d
en
ts
’
m
o
tiv
atio
n
[
1
7
]
.
Acc
o
r
d
in
g
to
p
r
ev
io
u
s
r
esear
ch
,
s
tu
d
en
ts
wh
o
h
a
d
G
M
in
ter
v
en
tio
n
s
s
h
o
wed
g
r
ea
t
er
lev
els
o
f
in
tr
in
s
ic
d
r
iv
e
an
d
a
g
r
e
ater
s
en
s
e
o
f
co
n
f
id
en
ce
in
th
ei
r
ca
p
ac
ity
to
o
v
er
co
m
e
c
h
allen
g
es
an
d
ad
v
an
ce
ac
ad
em
ically
.
L
ik
ewise,
J
o
h
n
s
to
n
-
W
ild
er
an
d
L
ee
[
1
8
]
d
is
co
v
e
r
ed
th
at
GM
in
ter
v
en
tio
n
s
h
ad
a
f
a
v
o
r
ab
le
im
p
a
ct
o
n
s
tu
d
en
ts
’
s
elf
-
ef
f
icac
y
b
elief
s
,
h
en
ce
au
g
m
en
tin
g
th
ei
r
will
to
p
er
s
ev
er
e
th
r
o
u
g
h
d
if
f
ic
u
lt
ac
tiv
ities
.
As
a
m
atter
o
f
f
ac
t,
it
ca
n
h
elp
p
r
o
tect
s
tu
d
en
ts
f
r
o
m
ac
ad
em
ic
s
tr
ess
b
y
en
co
u
r
ag
in
g
th
em
to
v
iew
f
ailu
r
e
as
an
o
p
p
o
r
tu
n
ity
to
lear
n
an
d
im
p
r
o
v
e
[
1
9
]
.
Fu
r
t
h
er
m
o
r
e,
Ha
r
b
e
r
t
[
2
0
]
lear
n
ed
th
at
s
tu
d
en
ts
w
h
o
b
eliev
e
th
ey
a
r
e
“
b
ad
at
m
ath
”
ap
p
r
o
ac
h
ev
e
r
y
wo
r
k
with
th
is
m
in
d
s
et,
f
ea
r
i
n
g
th
e
y
will
b
e
m
is
tak
en
.
Hen
ce
,
s
tu
d
en
ts
s
tar
t
to
with
d
r
aw
an
d
s
to
p
p
ar
ticip
atin
g
in
g
r
o
u
p
ac
tiv
ities
.
C
o
n
s
eq
u
en
tly
,
lear
n
e
r
s
o
f
ten
g
iv
e
u
p
b
ef
o
r
e
th
e
y
e
v
en
tr
y
b
ec
au
s
e
o
f
th
e
well
-
k
n
o
wn
m
a
th
s
ter
eo
ty
p
es a
n
d
t
h
eir
f
ea
r
o
f
h
u
m
iliatio
n
o
r
s
h
am
e
in
t
h
e
cl
ass
r
o
o
m
.
Usi
n
g
s
tr
u
ctu
r
al
eq
u
atio
n
m
o
d
elin
g
,
C
h
en
et
a
l.
[
2
1
]
d
is
co
v
er
ed
t
h
at
m
id
d
le
s
ch
o
o
l
s
t
u
d
en
ts
wh
o
h
av
e
a
GM
ar
e
s
u
b
s
tan
tially
m
o
r
e
lik
ely
to
ac
h
iev
e
ac
ad
em
ic
s
u
cc
ess
.
C
o
g
n
itiv
e
-
b
eh
a
v
io
r
al
ad
ap
tab
ilit
y
,
wh
ich
is
th
e
ca
p
ac
ity
o
f
s
tu
d
en
ts
to
m
o
d
if
y
th
eir
lea
r
n
in
g
s
tr
ateg
ies
an
d
p
er
s
ev
er
e
i
n
th
e
f
ac
e
o
f
ac
ad
e
m
ic
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
2
,
Ap
r
il
20
26
:
1
3
7
6
-
1
3
8
7
1380
d
if
f
icu
lties
,
in
f
lu
en
ce
s
t
h
is
r
elatio
n
s
h
ip
.
Ma
th
em
atica
l
r
e
s
ilien
ce
is
a
p
o
s
itiv
e
attitu
d
e
th
at
ar
is
es
wh
en
lear
n
er
s
f
in
d
m
ath
em
atics
d
if
f
icu
lt
an
d
th
ey
co
m
e
u
p
with
in
n
o
v
ativ
e
way
s
to
s
o
lv
e
th
e
p
r
o
b
lem
.
I
t
is
an
attr
ib
u
te,
b
eh
av
io
r
,
o
r
d
ee
d
th
at
r
esu
l
ts
f
r
o
m
ad
ju
s
tin
g
to
d
i
f
f
icu
lt
cir
cu
m
s
tan
ce
s
[
2
2
]
.
Ad
d
itio
n
ally
,
b
u
ild
in
g
m
ath
em
atica
l
r
esil
ien
ce
p
r
o
m
o
tes
s
tu
d
en
ts
’
co
n
f
id
en
ce
a
n
d
willin
g
n
ess
to
en
g
ag
e
in
m
at
h
em
atica
l
lear
n
in
g
wh
ile
s
af
eg
u
ar
d
in
g
th
eir
wellb
ein
g
d
u
r
in
g
th
e
s
tu
d
y
p
r
o
ce
s
s
[
2
3
]
.
Fu
r
th
er
m
o
r
e
,
r
esear
c
h
s
h
o
ws
th
at
alth
o
u
g
h
s
tu
d
en
ts
o
f
te
n
ca
r
r
y
n
eg
ativ
e
e
m
o
tio
n
s
f
r
o
m
p
ast
m
ath
em
atics
ex
p
er
ien
ce
s
,
th
e
s
e
f
ee
lin
g
s
ca
n
b
e
o
v
er
c
o
m
e
with
ap
p
r
o
p
r
iate
s
u
p
p
o
r
t.
Acc
o
r
d
in
g
t
o
s
tu
d
y
b
y
C
o
u
s
in
s
et
a
l.
[
2
4
]
,
lear
n
er
s
wer
e
ab
le
to
m
o
v
e
b
ey
o
n
d
f
ea
r
an
d
d
is
co
m
f
o
r
t
in
m
at
h
em
atics
wh
en
th
ey
r
ec
eiv
ed
s
en
s
itiv
e
en
c
o
u
r
a
g
em
en
t,
ef
f
e
ctiv
e
in
s
tr
u
ctio
n
a
l
s
tr
ateg
ies,
an
d
o
p
p
o
r
tu
n
iti
es
to
b
u
ild
th
eir
m
ath
em
atica
l
r
esil
ien
ce
.
GM
i
n
ter
v
en
tio
n
s
h
av
e
also
d
em
o
n
s
tr
ated
p
o
s
itiv
e
ef
f
ec
ts
o
n
ac
a
d
em
ic
p
er
f
o
r
m
a
n
ce
.
A
s
tu
d
y
by
B
u
r
n
ett
e
et
a
l.
[
2
5
]
r
ep
o
r
ted
s
ig
n
if
ican
t
im
p
r
o
v
em
en
ts
in
s
tu
d
en
ts
’
ac
h
iev
em
en
t
wh
en
th
ey
en
g
ag
ed
in
ac
tiv
ities
s
u
ch
as
g
o
al
-
s
ettin
g
,
ef
f
o
r
t
-
f
o
cu
s
ed
f
e
ed
b
ac
k
,
an
d
ex
p
licit
GM
in
s
t
r
u
ctio
n
.
Similar
ly
,
Mo
h
am
o
u
d
[
17
]
f
o
u
n
d
th
at
s
tu
d
en
ts
wh
o
p
ar
ticip
ated
in
G
M
p
r
o
g
r
am
s
attain
ed
h
ig
h
e
r
m
ath
em
atics
g
r
ad
es
th
an
th
o
s
e
wh
o
d
id
n
o
t.
I
n
t
h
e
p
r
esen
t
s
tu
d
y
,
T
S
em
er
g
ed
as
a
m
ea
n
in
g
f
u
l
p
r
e
d
icto
r
o
f
s
tu
d
en
ts
’
m
ath
em
atics
r
esil
ien
cy
in
p
r
o
b
lem
s
o
lv
in
g
,
s
u
p
p
o
r
ted
b
y
a
s
tatis
tically
s
i
g
n
if
ican
t
p
-
v
al
u
e
o
f
0
.
0
3
5
.
T
h
is
in
d
icate
s
s
tr
o
n
g
ev
id
en
ce
th
at
ef
f
ec
tiv
e
g
u
id
a
n
ce
f
r
o
m
teac
h
e
r
s
co
n
tr
ib
u
tes
t
o
s
tu
d
en
ts
’
ab
ilit
y
t
o
p
er
s
is
t
an
d
ad
a
p
t
wh
e
n
f
a
ce
d
with
m
ath
em
atica
l c
h
allen
g
es.
T
h
e
an
aly
s
is
r
ev
ea
ls
th
at
T
S
p
lay
s
a
m
ea
n
in
g
f
u
l
r
o
le
i
n
en
h
a
n
cin
g
s
tu
d
en
ts
’
m
at
h
em
atics
r
esil
ien
cy
.
T
h
e
r
eg
r
ess
io
n
co
ef
f
icien
t
o
f
0
.
1
0
7
in
d
icate
s
th
at
f
o
r
ev
e
r
y
o
n
e
-
u
n
it
i
n
cr
ea
s
e
in
TS
,
s
tu
d
en
t
r
esil
ien
cy
is
ex
p
ec
ted
to
im
p
r
o
v
e
b
y
0
.
1
0
7
u
n
its
,
ass
u
m
in
g
all
o
th
er
v
a
r
iab
les
r
em
ain
c
o
n
s
tan
t.
T
h
is
p
o
s
itiv
e
co
ef
f
icien
t
s
ig
n
if
ies
th
at
in
cr
ea
s
ed
s
u
p
p
o
r
t
f
r
o
m
teac
h
er
s
is
ass
o
ciate
d
with
s
tr
o
n
g
er
s
tu
d
en
t
r
esil
ien
ce
in
m
ath
em
atics.
T
h
e
p
r
ec
is
io
n
o
f
th
is
esti
m
at
e
is
s
u
p
p
o
r
ted
b
y
a
SE
o
f
0
.
0
5
1
,
an
d
th
e
t
-
v
al
u
e
o
f
2
.
1
1
6
p
r
o
v
id
es
f
u
r
th
e
r
ev
id
en
ce
th
at
th
e
co
ef
f
icien
t
s
ig
n
if
ican
tly
d
if
f
er
s
f
r
o
m
ze
r
o
,
r
ein
f
o
r
cin
g
th
e
v
ar
ia
b
le’
s
p
r
ed
i
ctiv
e
p
o
wer
.
L
iter
atu
r
e
also
s
u
p
p
o
r
ts
th
is
f
in
d
in
g
.
As
n
o
te
d
by
v
a
n
d
e
Po
l
et
a
l.
[2
6
]
,
s
ca
f
f
o
ld
i
n
g
in
v
o
lv
es
tim
ely
,
co
n
tin
g
en
t
ass
is
tan
ce
th
at
g
r
a
d
u
ally
f
a
d
es
as
lear
n
er
s
g
ain
co
m
p
eten
ce
,
an
d
th
is
p
r
o
ce
s
s
is
h
ig
h
ly
co
r
r
elate
d
with
h
o
w
ef
f
ec
tiv
ely
s
tu
d
e
n
ts
ap
p
ly
teac
h
er
s
u
p
p
o
r
t.
Stu
d
e
n
ts
ar
e
m
o
r
e
lik
ely
to
b
en
ef
it
f
r
o
m
s
ca
f
f
o
ld
in
g
wh
en
teac
h
er
s
p
r
o
v
id
e
tim
ely
,
r
esp
o
n
s
iv
e
g
u
id
an
ce
tailo
r
e
d
t
o
lear
n
er
s
’
n
ee
d
s
.
I
n
d
ee
d
,
t
h
e
attitu
d
es a
n
d
ex
p
er
ien
ce
s
th
at
s
tu
d
en
ts
h
av
e
with
m
ath
em
atics a
r
e
also
g
r
ea
tly
in
f
lu
en
ce
d
b
y
th
eir
teac
h
er
s
.
I
n
te
n
tio
n
all
y
o
r
u
n
in
ten
tio
n
ally
,
MA
ca
n
ca
u
s
e
teac
h
er
s
to
tr
a
n
s
m
it
th
eir
d
is
co
m
f
o
r
t
to
s
tu
d
en
ts
,
wh
ich
ca
n
ex
ac
er
b
a
te
n
eg
ativ
e
attitu
d
es
to
war
d
th
e
s
u
b
ject
an
d
lo
wer
th
e
lev
e
l
o
f
s
u
p
p
o
r
t
in
th
e
class
r
o
o
m
.
B
ec
au
s
e
it
m
ay
r
e
in
f
o
r
ce
b
r
o
a
d
er
s
o
cieta
l
s
ter
eo
ty
p
es
ab
o
u
t
m
ath
em
atica
l
ap
titu
d
e,
th
is
an
x
iety
m
ay
h
av
e
an
im
p
ac
t
o
u
ts
id
e
o
f
th
e
class
r
o
o
m
.
T
h
is
u
n
d
er
s
co
r
es
th
e
im
p
o
r
tan
ce
o
f
tr
ain
i
n
g
teac
h
er
s
to
ask
p
r
o
b
in
g
q
u
esti
o
n
s
,
ass
ess
s
t
u
d
en
t
c
o
m
p
r
e
h
en
s
io
n
,
an
d
ad
ju
s
t
s
u
p
p
o
r
t
ac
co
r
d
in
g
l
y
u
n
ti
l
s
tu
d
en
ts
ca
n
in
d
ep
en
d
en
tly
a
p
p
ly
th
eir
lea
r
n
in
g
[
2
7
]
.
As
a
m
atter
o
f
f
ac
t,
C
alo
r
et
a
l.
[2
8
]
s
tates
th
at,
b
y
p
r
o
v
id
in
g
s
o
cial
an
d
an
aly
tical
s
u
p
p
o
r
t
th
at
is
a
d
ap
ted
t
o
s
tu
d
en
ts
’
zo
n
es o
f
p
r
o
x
im
al
d
ev
elo
p
m
en
t,
m
ath
te
ac
h
er
s
ca
n
in
cr
ea
s
e
s
tu
d
en
t
en
g
ag
em
en
t
an
d
d
ee
p
en
th
eir
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
in
g
.
Ov
er
all,
th
e
m
o
d
el
id
en
t
if
ies
P
SS
,
GM
,
an
d
T
S
as
s
ig
n
if
ican
t
p
r
ed
icto
r
s
o
f
m
ath
em
atics
r
esil
ien
cy
,
af
f
ir
m
in
g
th
e
s
tu
d
y
’
s
p
r
o
p
o
s
itio
n
th
at
co
g
n
itiv
e,
p
s
y
ch
o
lo
g
ical,
an
d
s
o
cial
f
ac
to
r
s
co
llectiv
ely
in
f
lu
e
n
ce
s
tu
d
en
ts
’
ab
ilit
y
to
p
er
s
is
t
an
d
s
u
cc
ee
d
in
m
ath
em
atica
l p
r
o
b
lem
-
s
o
lv
in
g
.
3
.
2
.
Q
ua
lit
a
t
iv
e
f
ind
ing
s
T
h
e
r
esear
ch
e
r
s
co
n
d
u
cted
in
ter
v
iews
with
s
tu
d
en
ts
,
wh
o
ag
r
ee
d
t
o
b
e
in
ter
v
iewe
d
,
r
ea
ch
in
g
t
h
e
s
atu
r
atio
n
p
o
in
t
at
th
e
1
0
th
p
ar
ticip
an
t.
A
to
tal
o
f
4
9
s
i
g
n
if
ican
t
s
tatem
en
ts
wer
e
ex
tr
ac
ted
.
T
h
er
e
wer
e
3
3
f
o
r
m
u
lated
m
ea
n
in
g
s
an
d
th
r
ee
th
em
es
em
er
g
ed
f
r
o
m
t
h
e
an
aly
s
is
,
wh
ich
ar
e
as:
i
)
GM
an
d
p
o
s
itiv
e
lear
n
in
g
attitu
d
e;
ii
)
ac
tiv
e
p
r
o
b
lem
-
s
o
lv
in
g
s
tr
ateg
ies;
an
d
ii
i
)
SLE
an
d
TS
.
3
.
2
.
1
.
G
ro
wt
h
m
ind
s
et
a
nd
p
o
s
it
iv
e
lea
rning
a
t
t
it
ud
es
On
e
o
f
th
e
asp
ec
ts
th
at
is
ess
en
tial
to
s
u
cc
ess
f
u
lly
d
ea
l
with
m
ath
em
atics
p
r
o
b
lem
is
to
f
o
s
ter
GM
an
d
p
o
s
itiv
e
lear
n
in
g
attitu
d
es.
T
h
is
th
em
e
em
p
o
wer
s
s
tu
d
en
ts
to
tac
k
le
m
ath
w
ith
co
n
f
i
d
en
ce
a
n
d
willin
g
n
ess
to
lear
n
f
r
o
m
t
h
eir
ex
p
er
ien
ce
.
GM
en
a
b
les
s
tu
d
en
ts
to
s
ee
m
is
tak
es
an
d
s
etb
ac
k
s
n
o
t
as
f
ailu
r
e
b
u
t
as
an
o
p
p
o
r
tu
n
ity
to
lea
r
n
in
g
.
Po
s
itiv
e
lear
n
in
g
attitu
d
es
allo
ws
s
tu
d
en
ts
to
ap
p
r
o
ac
h
d
if
f
icu
lties
with
willin
g
n
ess
an
d
en
th
u
s
iasm.
I
m
p
o
r
ta
n
ce
o
f
GM
.
T
h
is
em
p
h
asize
th
at
m
ath
em
atics c
o
n
f
id
en
ce
is
n
o
t a
f
ix
ed
tr
ait,
b
u
t r
ath
er
a
s
k
ill
th
at
ca
n
b
e
d
e
v
elo
p
ed
.
C
o
n
f
id
en
ce
in
m
ath
is
a
s
k
ill
th
at
ca
n
b
e
lea
r
n
ed
an
d
im
p
r
o
v
ed
o
v
er
tim
e.
T
h
e
m
o
r
e
y
o
u
p
r
ac
tice
an
d
lear
n
f
r
o
m
m
is
tak
es,
th
e
m
o
r
e
c
o
n
f
id
e
n
t
y
o
u
will
b
ec
o
m
e
in
m
ath
.
T
h
is
co
n
ce
p
t
was
ar
ticu
lated
b
y
th
e
p
ar
ticip
an
ts
d
u
r
in
g
th
e
in
ter
v
iew.
T
h
ey
m
e
n
tio
n
ed
:
“
S
o
metime
s
I
feel
co
n
fid
en
t,
b
u
t
o
th
er
times
I
d
o
n
’
t.
I
t
d
ep
e
n
d
s
o
n
w
h
eth
er
I
ca
n
u
n
d
ers
ta
n
d
t
h
e
q
u
esti
o
n
s
ea
s
ily
a
n
d
if th
ey
m
a
ke
s
en
s
e
to
me.
”
(
I
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
B
ey
o
n
d
th
e
s
co
r
e:
a
s
eq
u
e
n
tia
l stu
d
y
o
n
th
e
p
r
ed
icto
r
s
o
f stu
d
en
t res
ilien
ce
in
…
(
R
o
a
r
A
.
C
a
lla
ma
n
)
1381
“
I
t
d
ep
en
d
s
.
I
feel
c
o
n
fid
en
t
if
I
ca
n
s
o
lve
a
p
r
o
b
lem
in
a
s
h
o
r
t
a
mo
u
n
t
o
f
time
a
n
d
a
ls
o
g
et
th
e
co
r
r
ec
t
a
n
s
w
er.
B
u
t
th
ere
a
r
e
times
w
h
en
yo
u
g
et
th
e
a
n
s
w
er
w
r
o
n
g
,
s
o
it
r
ea
lly
d
ep
en
d
s
o
n
th
e
s
itu
a
tio
n
o
n
w
h
eth
er I
’
m
c
o
n
fi
d
en
t o
r
u
n
s
u
r
e
a
b
o
u
t m
y
a
n
s
w
er.
”
(
I
2
)
“
A
ctu
a
lly,
s
o
metime
s
I
g
et
ex
cited
a
n
d
c
o
n
fid
en
t
s
o
lvin
g
t
h
ese
p
r
o
b
lems.
Like
r
ig
h
t
n
o
w
,
w
it
h
w
h
a
t
S
ir
S
ea
n
ta
u
g
h
t
u
s
a
b
o
u
t
p
r
o
b
a
b
ilit
y,
w
e
a
lr
ea
d
y
lea
r
n
ed
s
o
me
o
f
it
in
Gra
d
e
1
0
s
o
w
e
feel
mo
r
e
co
n
fid
en
t so
lvin
g
it e
ve
n
th
o
u
g
h
it
’
s
mo
r
e
d
iffi
cu
lt n
o
w
.
”
(
I
3
)
Mo
r
eo
v
er
,
th
e
im
p
o
r
tan
ce
o
f
a
GM
i
s
b
ein
g
h
ig
h
lig
h
ted
wh
er
e
ch
allen
g
es
ar
e
s
ee
n
as
av
en
u
e
to
lear
n
an
d
im
p
r
o
v
e.
C
la
s
s
r
o
o
m
s
th
at
allo
w
s
tu
d
en
ts
to
ex
p
r
ess
th
eir
s
tr
u
g
g
le
an
d
ex
am
i
n
e
“wr
o
n
g
”
an
s
wer
s
ar
e
s
ee
n
as
o
p
p
o
r
tu
n
ities
to
ex
p
lo
r
e
s
er
v
e
to
b
etter
s
u
p
p
o
r
t
a
n
d
m
o
tiv
ate
s
tu
d
e
n
ts
to
p
er
s
is
t
[
29
]
.
T
h
is
in
s
ig
h
t
allo
ws
s
tu
d
en
ts
to
v
iew
m
i
s
ta
k
es
as
s
tep
p
in
g
s
to
n
es
to
m
aster
y
,
f
o
s
ter
in
g
co
n
f
id
en
ce
in
t
h
eir
ab
ilit
y
to
lear
n
f
r
o
m
er
r
o
r
s
an
d
u
ltima
tely
s
u
c
ce
ed
in
m
ath
em
atics.
T
h
e
p
ar
t
icip
an
ts
p
o
in
ted
o
u
t:
“
S
o
metime
s
I
’
m
co
n
fid
e
n
t,
s
ir
,
a
n
d
o
th
er
times
I
’
m
n
o
t
b
ec
a
u
s
e
I
feel
like
my
a
n
s
w
er
mig
h
t
b
e
w
r
o
n
g
,
b
u
t
th
en
w
h
en
I
a
n
s
w
er,
it
tu
r
n
s
o
u
t
to
b
e
r
ig
h
t,
s
o
I
d
o
n
’
t
kn
o
w
w
h
a
t
to
th
in
k
a
b
o
u
t
myself.
”
(
I
4
)
“
Yes
,
s
ir
.
B
ec
a
u
s
e
yo
u
c
a
n
l
ea
r
n
fr
o
m
d
o
in
g
it.
S
o
,
b
y
j
u
s
t
tr
yin
g
,
I
th
in
k
I
c
a
n
fig
u
r
e
it
o
u
t.
S
o
,
it
’
s
n
o
t
a
p
r
o
b
lem
fo
r
me
t
o
fa
ce
n
ew p
r
o
b
lems.
”
(
I
5
)
T
h
is
f
i
n
d
i
n
g
is
s
u
p
p
o
r
te
d
b
y
t
h
e
s
tu
d
y
o
f
Aal
d
e
r
en
‐
S
m
ee
ts
et
a
l
.
[3
0
]
wh
ic
h
b
el
ie
v
es
t
h
at
t
h
e
a
d
o
p
ti
o
n
o
f
a
GM
co
u
l
d
h
el
p
s
t
u
d
e
n
t
s
to
m
ai
n
tai
n
a
r
e
lati
v
el
y
s
t
a
b
le
le
v
el
o
f
r
esil
ie
n
c
e
w
h
e
n
f
a
ci
n
g
f
ail
u
r
e
an
d
d
i
f
f
ic
u
lt
ies
in
le
ar
n
i
n
g
.
Als
o
,
Dwe
ck
[3
1
]
a
d
d
e
d
th
at
th
e
r
e
h
as
b
e
e
n
a
p
let
h
o
r
a
o
f
r
es
ea
r
c
h
s
h
o
wi
n
g
t
h
a
t
in
d
i
v
i
d
u
als
wit
h
a
GM
ar
e
m
o
r
e
li
k
e
ly
to
e
m
b
r
a
ce
c
h
al
le
n
g
es,
p
e
r
s
is
t
i
n
t
h
e
f
a
ce
o
f
s
e
tb
ac
k
s
,
an
d
v
i
ew
e
f
f
o
r
t
as
a
p
at
h
t
o
m
ast
er
y
.
Fu
r
t
h
er
m
o
r
e,
t
h
e
s
t
u
d
y
co
n
d
u
ct
ed
b
y
X
ia
o
e
t
a
l.
[3
2
]
i
m
p
li
es
t
h
a
t
e
n
c
o
u
r
a
g
i
n
g
s
tu
d
en
ts
t
o
h
a
v
e
a
GM
a
n
d
im
p
r
o
v
in
g
t
h
e
ir
g
e
n
e
r
a
l
we
ll
-
b
ei
n
g
t
h
r
o
u
g
h
co
n
s
t
r
u
ct
iv
e
te
ac
h
i
n
g
m
et
h
o
d
s
ca
n
i
n
c
r
e
ase
t
h
ei
r
m
o
ti
v
at
io
n
t
o
l
ea
r
n
,
p
r
o
m
o
te
t
h
ei
r
g
e
n
e
r
al
w
ell
b
e
in
g
,
an
d
e
v
en
t
u
all
y
r
esu
lt
in
b
et
te
r
ac
ad
e
m
ic
a
ch
ie
v
e
m
e
n
t
.
Dev
elo
p
in
g
p
o
s
itiv
e
attitu
d
es
to
war
d
s
ch
allen
g
es.
C
u
ltiv
atin
g
a
p
o
s
itiv
e
attitu
d
e
to
war
d
s
c
h
allen
g
es
is
k
ey
to
u
n
lo
c
k
in
g
s
u
cc
ess
in
m
ath
.
T
h
is
m
ea
n
s
v
iewin
g
d
if
f
icu
lties
as
o
p
p
o
r
t
u
n
ities
to
lear
n
an
d
g
r
o
w,
r
ath
er
th
an
an
o
b
s
tacle
.
Stu
d
e
n
ts
wh
o
em
b
r
ac
e
ch
allen
g
es
c
an
d
ev
elo
p
a
s
en
s
e
o
f
ex
cite
m
en
t
ab
o
u
t
tack
lin
g
n
ew
p
r
o
b
lem
s
.
T
h
ey
s
ee
m
is
tak
es
as
n
atu
r
al
p
ar
t
o
f
t
h
e
lear
n
in
g
p
r
o
ce
s
s
,
n
o
t
a
r
e
f
lectio
n
o
f
th
eir
in
tellig
en
ce
.
As a
m
atter
o
f
f
ac
t,
th
is
s
u
b
th
e
m
e
was b
r
o
u
g
h
t u
p
b
y
t
h
e
p
ar
t
icip
an
ts
d
u
r
in
g
th
e
in
ter
v
iew.
Par
ticip
an
ts
s
aid
:
“
A
ch
a
n
ce
to
lea
r
n
a
n
d
g
r
o
w
b
ec
a
u
s
e
I
kn
o
w
th
a
t
w
e
a
r
e
n
o
t
p
erfect
a
n
d
it
is
n
o
r
ma
l
fo
r
u
s
to
ma
ke
mis
ta
ke
s
a
s
lo
n
g
a
s
w
e
a
r
e
s
u
p
p
o
s
ed
to
d
o
it b
ec
a
u
s
e
w
e
w
ill s
ti
ll imp
r
o
ve
.
”
(
I
3
)
“
A
t
fir
s
t,
I
’
ll
o
f
co
u
r
s
e
b
e
d
is
a
p
p
o
in
te
d
a
t
myself
a
n
d
I
’
ll
s
ta
r
t
d
o
u
b
tin
g
myself,
b
u
t
t
h
a
t
d
o
esn
’
t
mea
n
th
a
t I
ca
n
’
t
g
r
o
w
a
n
d
le
a
r
n
a
lo
t fro
m
it.
”
(
I
1
0
)
T
h
ese
claim
s
wer
e
s
u
p
p
o
r
ted
b
y
th
e
o
th
er
p
ar
ticip
an
t
wh
o
s
ee
s
s
etb
ac
k
s
a
s
an
o
p
p
o
r
t
u
n
ity
to
co
r
r
ec
t
m
is
tak
es,
an
d
to
lear
n
less
o
n
s
.
T
h
ey
s
tated
:
“
F
o
r
me,
it
is
a
ch
a
n
ce
t
o
lea
r
n
a
n
d
g
r
o
w
b
ec
a
u
s
e
o
f
co
u
r
s
e,
a
s
th
e
s
a
yin
g
g
o
es,
less
o
n
s
ca
n
b
e
lea
r
n
ed
fr
o
m
mis
ta
ke
s
.
”
(
I
2
)
“
I
s
ee
it
a
s
a
n
o
p
p
o
r
tu
n
ity
to
g
r
o
w
,
s
ir
.
I
t
is
b
ec
a
u
s
e
it
h
elp
ed
me
to
co
r
r
ec
t
my
w
r
o
n
g
s
a
n
d
it
’
s
a
ls
o
a
ch
a
llen
g
e
fo
r
me
to
b
e
mo
r
e
d
etermin
ed
in
s
o
lvin
g
m
o
r
e
ma
th
p
r
o
b
lems.
”
(
I
5
)
“
I
ta
ke
it a
s
a
lea
r
n
b
ec
a
u
s
e
e
ve
r
y
d
a
y
th
ere
is
a
n
ew w
a
y
to
lea
r
n
.
”
(
I
6
)
T
h
e
s
tu
d
y
o
f
Hwa
n
g
an
d
So
n
[3
3
]
s
u
p
p
o
r
ts
th
is
claim
s
tatin
g
th
at
s
tu
d
en
ts
with
p
o
s
itiv
e
attitu
d
es
ar
e
m
o
r
e
lik
el
y
to
s
u
cc
ee
d
in
m
at
h
em
atics.
T
h
ey
em
p
h
asized
th
at
attitu
d
e
to
war
d
s
m
ath
e
m
atics
h
as
a
s
ig
n
i
f
ican
t
r
elatio
n
s
h
ip
with
m
ath
em
atic
s
ac
h
iev
em
en
t.
I
n
ad
d
itio
n
,
a
s
tu
d
en
t
’
s
p
o
s
itiv
e
attitu
d
e
t
o
war
d
s
m
ath
em
atics
m
ig
h
t
in
cr
ea
s
e
th
eir
m
ath
em
atics
-
r
elate
d
h
ip
p
o
ca
m
p
al
ac
tiv
ity
an
d
m
em
o
r
y
-
r
etr
iev
al
a
ctiv
ity
in
th
e
b
r
ain
,
wh
ich
co
u
ld
h
elp
th
e
m
to
ac
h
i
ev
e
h
ig
h
m
ath
em
atics p
er
f
o
r
m
an
ce
[
3
4
].
3
.
2
.
2
.
Act
iv
e
pro
blem
-
s
o
lv
in
g
s
t
ra
t
eg
ies
On
e
o
f
th
e
th
em
es
th
at
em
er
g
ed
wh
en
s
tu
d
en
ts
ar
e
ask
o
n
th
e
f
ac
to
r
s
th
at
h
elp
th
em
b
u
ild
th
eir
r
esil
ien
cy
in
s
o
lv
in
g
m
ath
em
a
tics
p
r
o
b
lem
s
is
ac
tiv
e
p
r
o
b
lem
-
s
o
lv
in
g
.
T
h
e
th
em
e
h
ig
h
lig
h
ts
th
e
im
p
o
r
tan
ce
o
f
d
e
v
elo
p
in
g
an
d
u
tili
zin
g
ef
f
ec
ti
v
e
p
r
o
b
lem
-
s
o
lv
in
g
s
tr
ateg
ies
in
m
ath
em
atics.
I
m
p
o
r
tan
c
e
o
f
u
n
d
er
s
tan
d
i
n
g
th
e
p
r
o
b
lem
.
Un
d
er
s
tan
d
in
g
th
e
p
r
o
b
lem
its
elf
is
th
e
f
o
u
n
d
atio
n
to
s
u
cc
ess
f
u
lly
s
o
lv
e
th
e
p
r
o
b
lem
.
T
h
e
s
u
b
th
em
es
em
p
h
asize
th
at
s
tu
d
en
ts
n
ee
d
to
g
r
asp
co
r
e
c
o
n
ce
p
ts
,
d
ec
ip
h
er
th
e
wo
r
d
in
g
a
n
d
v
is
u
alizin
g
th
e
p
r
o
b
lem
.
T
h
is
was e
m
p
h
asis
wh
en
o
n
e
p
ar
ticip
an
t m
e
n
tio
n
ed
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
2
,
Ap
r
il
20
26
:
1
3
7
6
-
1
3
8
7
1382
“
I
f
th
e
p
r
o
b
lem
is
a
w
o
r
d
p
r
o
b
lem,
I
a
lw
a
ys
tr
y
to
u
n
d
ers
ta
n
d
th
e
p
r
o
b
lem
fir
s
t
to
ma
ke
it
ea
s
ie
r
to
s
o
lve
a
n
d
g
et
th
e
a
n
s
w
er.
I
f
th
e
q
u
esti
o
n
s
a
lr
ea
d
y
h
a
ve
n
u
mb
ers
g
iven
,
th
e
n
I
a
s
k
fo
r
h
elp
a
n
d
ch
ec
k
my
n
o
tes
to
s
ee
w
h
a
t
th
e
s
o
lu
tio
n
is
fo
r
th
a
t
s
p
ec
ific
q
u
esti
o
n
.
I
u
s
u
a
lly
id
en
tify
th
e
g
iven
in
fo
r
ma
tio
n
a
n
d
w
h
a
t is b
ein
g
a
s
ke
d
in
th
e
p
r
o
b
lem.
”
(
I
1
)
B
y
tak
in
g
tim
e
to
tr
u
ly
u
n
d
er
s
tan
d
th
e
p
r
o
b
lem
,
s
tu
d
en
ts
ca
n
ap
p
r
o
ac
h
s
t
r
ateg
ically
an
d
ch
o
o
s
e
th
e
m
o
s
t
ap
p
r
o
p
r
iate
s
o
lu
tio
n
m
e
th
o
d
.
T
h
is
is
s
u
p
p
o
r
ted
b
y
th
e
s
tu
d
y
o
f
Sin
ag
a
et
a
l.
[3
5
]
wh
ich
p
o
s
ited
th
at
s
tu
d
en
ts
’
p
r
o
b
lem
-
s
o
lv
in
g
u
n
d
er
s
tan
d
in
g
h
as
a
s
ig
n
if
ican
t
in
f
lu
en
ce
o
n
m
at
h
em
atics
lear
n
in
g
.
Hen
ce
,
wh
e
n
s
tu
d
en
ts
h
av
e
a
m
o
r
e
p
o
s
itiv
e
p
er
ce
p
tio
n
o
f
th
e
m
i
n
d
s
et
en
v
ir
o
n
m
e
n
t,
th
ey
ar
e
m
o
r
e
lik
e
ly
to
ac
h
iev
e
b
etter
r
esu
lts
[
3
6
].
D
e
v
e
l
o
p
i
n
g
P
SS
,
t
h
i
s
s
u
b
t
h
e
m
e
g
o
e
s
b
e
y
o
n
d
s
i
m
p
l
y
k
n
o
w
i
n
g
h
o
w
t
o
s
o
l
v
e
p
r
o
b
l
e
m
s
.
I
t
f
o
c
u
s
e
s
o
n
t
h
e
v
a
r
i
o
u
s
s
t
r
a
t
e
g
i
e
s
a
n
d
s
k
i
l
ls
s
tu
d
e
n
t
s
d
e
v
e
l
o
p
t
o
s
o
l
v
e
p
r
o
b
le
m
s
i
n
m
a
t
h
e
m
at
i
cs
e
f
f
e
ct
i
v
e
ly
.
I
t
e
m
p
h
a
s
i
z
es
t
h
e
i
m
p
o
r
t
a
n
c
e
o
f
m
o
v
i
n
g
b
e
y
o
n
d
r
o
t
e
m
e
m
o
r
i
z
a
ti
o
n
a
n
d
t
o
w
a
r
d
s
a
m
o
r
e
f
l
e
x
i
b
le
a
n
d
a
d
a
p
t
a
b
l
e
a
p
p
r
o
a
c
h
e
d
.
T
h
e
s
e
i
n
c
l
u
d
e
s
p
r
a
ct
i
c
e
a
n
d
e
f
f
o
r
t
,
s
t
r
a
t
e
g
i
c
u
s
e
o
f
r
es
o
u
r
c
e
s
,
c
o
n
n
e
ct
i
n
g
n
e
w
p
r
o
b
l
e
m
s
t
o
p
r
i
o
r
k
n
o
w
l
e
d
g
e
,
a
n
a
l
y
z
i
n
g
m
i
s
t
a
k
es
a
n
d
d
e
v
e
l
o
p
i
n
g
s
e
l
f
-
l
e
a
r
n
i
n
g
h
a
b
i
ts
.
I
n
e
s
s
e
n
c
e
,
r
e
g
u
l
a
r
l
y
e
n
g
a
g
i
n
g
wi
t
h
d
i
v
e
r
s
e
p
r
o
b
l
e
m
s
a
l
l
o
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s
t
u
d
e
n
ts
t
o
s
o
l
i
d
i
f
y
t
h
e
i
r
u
n
d
er
s
t
a
n
d
i
n
g
o
f
m
a
t
h
e
m
a
t
i
c
al
c
o
n
c
e
p
t
s
a
n
d
t
h
e
i
r
a
p
p
l
i
c
at
i
o
n
s
.
St
u
d
e
n
t
s
’
e
f
f
o
r
t
a
n
d
p
r
a
c
t
i
c
e
i
n
s
o
l
v
i
n
g
p
r
o
b
l
e
m
s
l
ea
d
t
o
k
n
o
w
l
e
d
g
e
g
a
i
n
.
T
h
i
s
w
as
h
i
g
h
l
i
g
h
t
e
d
w
h
e
n
o
n
e
o
f
t
h
e
p
a
r
t
i
c
i
p
a
n
ts
s
t
a
t
e
d
:
“
Yes
,
if
yo
u
d
o
n
’
t
p
u
t
in
effo
r
t,
yo
u
d
o
n
’
t
tr
y
to
s
o
lve
p
r
o
b
lems,
a
n
d
yo
u
d
o
n
’
t
p
r
a
ctice
h
o
w
to
s
o
lve
th
em,
h
o
w
ca
n
y
o
u
g
a
in
th
e
kn
o
w
led
g
e
to
s
o
lve
o
th
er q
u
est
io
n
s
?
”
(
I
3
)
Ap
a
r
t
f
r
o
m
t
h
is
,
p
a
r
t
ici
p
an
ts
a
ls
o
e
x
cla
im
ed
t
h
at
s
t
r
at
eg
i
c
u
s
e
o
f
r
eso
u
r
c
es
lea
d
s
s
t
u
d
e
n
ts
t
o
c
o
n
f
r
o
n
t
ch
all
en
g
es
.
T
h
is
i
n
cl
u
d
es
t
ex
tb
o
o
k
a
n
d
n
o
t
es
r
e
f
e
r
e
n
ce
s
,
o
n
li
n
e
t
o
o
ls
a
n
d
p
ee
r
a
n
d
t
ea
ch
e
r
g
u
i
d
a
n
c
e.
T
h
ey
s
a
id
:
“
My
s
tr
a
teg
y
is
to
ta
ke
n
o
tes
o
n
o
u
r
less
o
n
s
,
a
n
d
t
h
en
w
h
en
w
e
h
a
ve
a
ctivities,
I
r
efer
b
a
ck
to
my
n
o
tes to
s
ee
h
o
w
to
a
n
s
w
er th
e
m.
”
(
I
4
)
“
I
w
o
u
ld
a
s
k
th
e
tea
ch
er
to
h
e
lp
me
w
i
th
th
a
t
b
ec
a
u
s
e
it
’
s
th
e
tea
ch
er
’
s
d
u
ty
to
h
elp
me
w
i
th
my
d
iffi
cu
lties
,
esp
ec
ia
lly
in
ma
th
.
S
o
,
if
th
e
tea
c
h
er
is
a
va
ila
b
l
e
to
tea
ch
a
n
d
g
u
id
e
me,
th
e
n
I
’
m
u
p
fo
r
it.
”
(I5
)
“
Wh
en
I
g
o
h
o
me
a
n
d
I
s
till
ca
n
’
t
u
n
d
ers
ta
n
d
th
e
eq
u
a
tio
n
its
elf,
I
’
ll
fin
d
tu
to
r
ia
l
s
fr
o
m
Yo
u
Tu
b
e.
”
(
1
0
)
T
h
e
r
esu
lt
o
f
th
e
s
tu
d
y
is
co
n
tr
ar
y
to
th
e
f
in
d
in
g
s
o
f
Dix
it
et
a
l.
[3
7
]
.
I
t
r
e
v
ea
led
t
h
at
s
tu
d
en
ts
wh
o
u
s
e
th
e
co
n
v
en
tio
n
al
s
elf
-
r
eg
u
lated
lear
n
in
g
ap
p
r
o
ac
h
o
n
l
y
p
ay
atten
tio
n
to
t
h
e
r
esu
lts
o
f
test
s
an
d
f
ee
d
b
ac
k
p
r
o
v
id
e
d
b
y
th
ei
r
teac
h
er
.
T
h
e
y
s
eld
o
m
h
av
e
b
e
h
av
io
r
s
o
f
lo
o
k
in
g
at
th
e
s
u
p
p
lem
en
tar
y
m
ater
ials
,
ad
d
in
g
o
r
d
eletin
g
n
o
tes.
Mo
r
eo
v
er
,
tak
i
n
g
in
itiativ
es
to
lear
n
in
d
ep
en
d
en
tly
s
tr
en
g
th
en
s
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies.
T
h
is
co
m
p
r
is
es
ac
tiv
ely
s
ee
k
in
g
o
u
t
ad
d
itio
n
al
p
r
ac
tice
p
r
o
b
le
m
s
,
ex
p
lo
r
in
g
alter
n
ativ
e
s
o
l
u
tio
n
m
eth
o
d
s
an
d
r
esear
ch
in
g
r
ele
v
an
t c
o
n
ce
p
ts
an
d
f
o
r
m
u
las to
d
ee
p
en
u
n
d
e
r
s
tan
d
in
g
.
Par
ticip
an
ts
r
esp
o
n
d
e
d
:
“
F
ir
s
t,
I
r
ec
a
ll
w
h
a
t
S
ir
S
ea
n
ta
u
g
h
t
u
s
,
d
iffer
en
t
to
p
ics,
a
n
d
th
en
I
crea
te
my
o
w
n
q
u
esti
o
n
s
th
a
t
a
r
e
mo
r
e
d
iffi
cu
lt to
s
ee
if I
ca
n
a
n
s
w
er th
em
o
r
n
o
t.
”
(
I
3
)
“
I
ju
s
t d
o
s
elf
-
lea
r
n
in
g
n
o
w
b
e
ca
u
s
e
ma
th
cla
s
s
is
n
’
t th
a
t g
o
o
d
a
n
ym
o
r
e,
s
ir
.
”
(
I
7
)
L
ea
r
n
in
g
a
s
in
g
le
tech
n
iq
u
e
b
y
its
elf
is
n
o
t
th
e
g
o
al
o
f
i
m
p
r
o
v
i
n
g
p
r
o
b
lem
-
s
o
lv
in
g
a
b
ilit
ies
as
a
wh
o
le.
I
t
in
v
o
lv
es
d
ev
elo
p
i
n
g
an
ap
p
r
o
ac
h
th
at
b
len
d
s
th
ese
m
an
y
co
m
p
o
n
e
n
ts
in
a
f
lex
ib
le
an
d
ad
ap
tiv
e
m
an
n
er
.
T
h
e
r
esu
lt
is
i
n
l
in
e
with
th
e
s
tu
d
y
o
f
Har
s
ela
an
d
Asi
h
[
1
4
]
wh
o
v
iewe
d
th
at
t
h
e
ac
h
iev
e
m
en
t
o
f
s
tu
d
en
ts
’
ab
ilit
y
to
s
o
l
v
e
m
ath
em
atica
l
p
r
o
b
lem
s
af
f
e
cts
th
eir
r
esil
ien
cy
in
m
ath
em
atics.
Similar
ly
,
th
e
ef
f
icac
y
o
f
p
r
o
b
lem
-
b
ased
lear
n
in
g
in
im
p
r
o
v
in
g
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
i
es
is
d
em
o
n
s
tr
ated
b
y
th
e
ef
f
icien
t
ap
p
licatio
n
o
f
ac
tiv
e
lear
n
in
g
tech
n
i
q
u
es
to
s
k
ill
d
ev
elo
p
m
e
n
t,
wh
ich
is
b
ec
o
m
in
g
m
o
r
e
a
n
d
m
o
r
e
im
p
o
r
tan
t
i
n
th
e
m
o
d
e
r
n
w
o
r
l
d
[
3
7
]
.
As
a
wh
o
le,
b
y
m
aster
in
g
th
ese
ac
tiv
e
s
tr
ateg
ies,
s
tu
d
en
ts
ap
p
r
o
ac
h
m
at
h
with
co
n
f
id
en
ce
,
f
lex
ib
ilit
y
,
a
n
d
th
e
a
b
ilit
y
to
f
in
d
ef
f
ec
tiv
e
s
o
lu
tio
n
s
to
an
y
p
r
o
b
lem
th
ey
en
co
u
n
ter
.
3
.
2
.
3
.
Su
pp
o
rt
iv
e
lea
rning
env
iro
nm
ent
a
nd
t
ea
cher
s
ca
f
f
o
ldi
ng
T
h
is
th
em
e
ca
p
tu
r
es th
e
im
p
o
r
tan
ce
th
e
r
o
le
a
SLE
an
d
ef
f
ec
tiv
e
T
S p
lay
in
f
o
s
ter
in
g
m
ath
r
esil
ien
ce
a
n
d
s
tu
d
en
ts
’
s
u
cc
ess
.
T
h
is
is
n
o
t
a
o
n
e
-
s
id
ed
af
f
air
,
b
u
t
r
at
h
er
a
co
llab
o
r
ativ
e
ef
f
o
r
t
th
at
em
p
o
wer
s
s
tu
d
en
ts
to
th
r
iv
e
in
s
o
lv
in
g
m
ath
em
ati
cs
p
r
o
b
lem
s
.
T
h
e
th
em
e
co
m
p
r
is
es
th
r
ee
s
u
b
th
em
es:
clea
r
c
o
m
m
u
n
icatio
n
an
d
in
s
tr
u
ctio
n
,
en
g
ag
in
g
ac
tiv
ities
an
d
p
er
s
o
n
alize
d
s
u
p
p
o
r
t,
an
d
ac
ce
s
s
to
r
eso
u
r
ce
s
an
d
s
u
p
p
o
r
t.
C
lear
co
m
m
u
n
icatio
n
an
d
in
s
tr
u
ctio
n
.
A
SLE
s
tar
ts
with
a
f
o
u
n
d
atio
n
o
f
clea
r
co
m
m
u
n
i
ca
tio
n
an
d
in
s
tr
u
ctio
n
.
C
o
m
p
le
x
m
ath
e
m
atica
l
co
n
ce
p
ts
ca
n
b
e
d
au
n
tin
g
.
C
lear
ex
p
lan
atio
n
s
th
at
b
r
e
ak
d
o
w
n
to
p
ics
in
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t
J
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al
&
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es E
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c
I
SS
N:
2252
-
8
8
2
2
B
ey
o
n
d
th
e
s
co
r
e:
a
s
eq
u
e
n
tia
l stu
d
y
o
n
th
e
p
r
ed
icto
r
s
o
f stu
d
en
t res
ilien
ce
in
…
(
R
o
a
r
A
.
C
a
lla
ma
n
)
1383
m
an
ag
ea
b
le
s
tep
s
an
d
u
tili
ze
co
n
cr
ete
ex
am
p
les
ar
e
ess
en
tials
f
o
r
s
tu
d
en
t
u
n
d
er
s
tan
d
in
g
.
T
h
e
p
a
r
ticip
an
ts
m
an
if
est th
e
s
am
e
ex
p
er
ie
n
ce
d
,
as th
ey
m
e
n
tio
n
ed
:
“
I
’
m
imp
r
o
vin
g
b
ec
a
u
s
e
o
f o
u
r
tea
ch
er.
B
efo
r
e,
I
d
id
n
’
t fe
el
g
o
o
d
in
m
a
th
,
b
u
t n
o
w
o
u
r
tea
ch
er is
ve
r
y
a
p
p
r
o
a
c
h
a
b
le
a
n
d
ea
s
y
t
o
ta
lk
to
.
I
f
y
o
u
h
a
ve
a
n
y
c
o
n
f
u
s
in
g
q
u
esti
o
n
s
,
h
e
ca
n
ea
s
ily
ex
p
la
in
th
em,
a
n
d
h
is
ex
a
mp
les a
r
e
ve
r
y
clea
r
a
n
d
ea
s
y
to
u
n
d
ers
ta
n
d
.
”
(
I
1
)
“
Ou
r
tea
ch
er
ex
p
l
a
in
s
th
in
g
s
ve
r
y
w
ell,
ve
r
y
clea
r
ly.
Yo
u
c
a
n
’
t
h
elp
b
u
t
u
n
d
ers
ta
n
d
b
ec
a
u
s
e
h
is
ex
a
mp
les
a
r
e
d
ir
ec
tly
r
ela
ted
to
th
e
less
o
n
a
n
d
in
cl
u
d
e
ev
ery
s
tep
,
ev
en
s
ma
ll
d
eta
ils
.
He
ela
b
o
r
a
tes o
n
h
is
ex
p
l
a
n
a
tio
n
s
s
o
I
ca
n
u
n
d
ers
ta
n
d
th
em.
”
(
I
2
)
B
y
estab
lis
h
in
g
th
is
,
teac
h
er
s
eq
u
ip
s
tu
d
e
n
ts
with
a
s
o
lid
f
o
u
n
d
atio
n
f
o
r
u
n
d
er
s
tan
d
in
g
m
ath
em
atics.
T
h
is
wo
u
ld
p
r
o
v
id
e
c
o
n
f
id
en
ce
to
s
tu
d
en
ts
to
f
ac
ed
d
if
f
icu
lt m
at
h
em
atics p
r
o
b
lem
s
.
E
n
g
ag
in
g
ac
tiv
ities
an
d
p
er
s
o
n
alize
d
s
u
p
p
o
r
t
.
T
h
is
s
u
b
th
em
e
em
p
h
asized
th
at
in
c
o
r
p
o
r
ati
n
g
en
g
ag
in
g
ac
tiv
ities
an
d
p
e
r
s
o
n
alize
d
s
u
p
p
o
r
t
cr
ea
tes
an
in
c
lu
s
iv
e
lear
n
in
g
e
n
v
ir
o
n
m
en
t
wh
er
e
s
tu
d
en
ts
f
ee
l
co
m
f
o
r
ta
b
le
tak
in
g
r
is
k
s
,
ask
in
g
q
u
esti
o
n
s
,
a
n
d
p
e
r
s
is
tin
g
th
r
o
u
g
h
ch
allen
g
es.
L
ea
r
n
in
g
m
ath
em
atics
d
o
es
n
o
t
h
av
e
to
b
e
d
r
y
an
d
m
o
n
o
to
n
o
u
s
.
Activ
ities
lik
e
g
am
es,
h
an
d
s
-
o
n
p
r
o
jects,
an
d
g
r
o
u
p
wo
r
k
ca
n
m
ak
e
t
h
e
lear
n
in
g
p
r
o
ce
s
s
m
o
r
e
in
ter
a
ctiv
e
an
d
en
jo
y
ab
le.
T
h
is
w
as
p
r
o
p
o
u
n
d
ed
b
y
th
e
p
ar
tic
ip
an
ts
wh
en
th
ey
m
en
tio
n
ed
i
n
th
e
in
ter
v
iew.
T
h
ey
s
aid
:
“
Yes
,
esp
ec
ia
lly
w
h
en
h
e
g
ive
s
p
o
p
q
u
iz
z
es.
My
cla
s
s
ma
tes,
in
s
tea
d
o
f
feelin
g
s
leep
y,
g
et
ex
cited
b
ec
a
u
s
e
o
f th
e
p
o
p
q
u
iz
z
es.
”
(
I
3
)
“
He
’
s
ve
r
y
ea
s
yg
o
in
g
,
b
u
t
h
is
myster
y
b
o
xe
s
mo
tiva
te
me
to
a
n
s
w
er
b
ec
a
u
s
e
h
e
h
a
s
s
o
meth
in
g
to
g
ive
(
a
s
a
r
ewa
r
d
)
.
”
(
I
2
)
“
Yes
s
ir
,
th
e
a
ctivities
yo
u
g
ive
u
s
a
r
e
th
in
g
s
w
e
ca
n
a
p
p
l
y
to
o
u
r
s
elve
s
,
s
ir
,
like
th
e
co
in
to
s
s
a
ctivity.
”
(
I
4
)
Me
an
wh
ile,
a
SLE
r
ec
o
g
n
izes
in
d
iv
id
u
al
n
ee
d
s
.
T
ea
ch
er
s
wh
o
p
r
o
v
id
e
d
if
f
er
e
n
tiated
in
s
tr
u
ctio
n
ca
n
ca
ter
to
d
if
f
er
en
t
lear
n
in
g
s
ty
les
an
d
p
ac
es.
T
h
is
m
ay
b
e
in
v
o
lv
e
p
r
o
v
id
i
n
g
ad
d
iti
o
n
al
ex
p
lan
atio
n
s
,
alter
n
ativ
e
r
eso
u
r
ce
s
,
o
r
in
d
i
v
id
u
alize
d
f
ee
d
b
ac
k
to
s
tu
d
en
ts
.
Par
ticip
an
ts
m
en
tio
n
ed
:
“
I
like
h
o
w
h
e
te
a
ch
es
me.
He
’
ll
s
a
y
s
o
meth
in
g
like
‘
I
8
,
th
is
is
h
o
w
yo
u
c
a
n
s
o
lve
th
is
eq
u
a
tio
n
,
’
a
n
d
I
ca
n
r
ea
lly
ca
tc
h
u
p
b
ec
a
u
s
e
I
feel
like
S
ir
is
a
ve
r
y
g
o
o
d
tea
c
h
er.
He
r
ea
lly
tr
ies
h
is
b
est
to
ex
p
la
in
th
in
g
s
to
h
is
s
tu
d
en
ts
.
”
(
I
8
)
“
He
p
r
o
vid
es a
file wi
th
co
n
ten
t rela
ted
to
th
e
to
p
ic,
a
n
d
th
e
in
fo
r
ma
tio
n
th
ere
is
clea
r
er.
”
(
I
1
)
Acc
ess
to
r
eso
u
r
ce
s
an
d
s
u
p
p
o
r
t.
T
h
is
s
u
b
th
em
e
u
n
d
e
r
s
co
r
es
th
e
im
p
o
r
tan
ce
o
f
p
r
o
v
id
i
n
g
s
tu
d
en
ts
with
th
e
to
o
ls
th
ey
n
ee
d
to
t
h
r
iv
e
in
m
ath
e
m
atics.
T
h
is
in
clu
d
es
clea
r
i
n
s
tr
u
ctio
n
al
g
u
i
d
es
f
o
r
in
d
e
p
en
d
e
n
t
p
r
ac
tice,
ac
ce
s
s
to
ex
ter
n
al
lea
r
n
in
g
r
eso
u
r
ce
s
th
at
ca
ter
to
d
if
f
er
en
t
lear
n
i
n
g
s
ty
les,
v
is
u
al
aid
s
lik
e
d
iag
r
am
s
an
d
f
o
r
m
u
las
f
o
r
r
e
f
er
en
ce
,
a
n
d
a
teac
h
er
wh
o
is
co
n
s
is
ten
tly
av
ailab
le
f
o
r
q
u
esti
o
n
s
a
n
d
g
u
id
an
ce
.
T
h
e
s
tu
d
y
of
v
an
d
e
Po
l
et
a
l.
[2
6
]
clar
if
ies
th
e
s
ca
f
f
o
ld
in
g
p
r
o
ce
s
s
an
d
its
p
o
ten
tial
im
p
ac
t
o
n
s
tu
d
en
ts
’
lear
n
in
g
.
As
a
m
atter
o
f
f
ac
t,
t
h
is
s
u
b
th
em
e
was b
r
o
u
g
h
t
u
p
b
y
th
e
p
ar
ticip
an
ts
d
u
r
in
g
t
h
e
in
ter
v
iew.
T
h
e
y
s
aid
:
“
Uh
m,
like
th
e
g
u
id
es S
ir
s
en
d
s
u
s
o
n
h
o
w
to
s
o
lve
a
p
a
r
ticu
l
a
r
q
u
esti
o
n
.
”
(
I
3
)
“
S
o
metime
s
h
e
’
ll
g
ive
u
s
a
Yo
u
Tu
b
e
s
o
u
r
ce
to
u
n
d
ers
ta
n
d
th
e
co
n
ce
p
t
clea
r
ly
o
r
th
e
ea
s
i
est
w
a
y
to
fig
u
r
e
it o
u
t.
S
o
metime
s
,
h
e
ex
p
la
in
s
it h
ims
elf.
”
(
I
5
)
“
Th
is
s
eme
s
te
r
,
ye
s
,
h
e
s
en
d
s
ima
g
es
w
ith
fo
r
mu
la
s
o
n
h
o
w
to
s
o
lve
p
r
o
b
lems
a
n
d
ex
p
l
a
in
s
w
h
a
t
th
e
to
p
ic
is
a
b
o
u
t.
”
(
I
6
)
“
Ma
yb
e
h
e
’
s
g
o
o
d
,
s
ir
,
a
lth
o
u
g
h
h
e
mig
h
t
n
o
t
a
lw
a
ys
b
e
t
h
ere
to
tea
ch
u
s
,
s
ir
.
S
o
metime
s
,
h
e
g
ives ju
s
t o
n
e
ex
a
mp
le,
th
e
n
a
f
ter th
a
t,
h
e
g
ives u
s
a
q
u
iz
.
”
(
I
7
)
B
y
p
r
o
v
id
i
n
g
s
tu
d
e
n
ts
with
ac
ce
s
s
to
a
v
ar
iety
o
f
r
eso
u
r
ce
s
an
d
en
s
u
r
i
n
g
co
n
s
is
ten
t
s
u
p
p
o
r
t,
teac
h
er
s
em
p
o
wer
th
em
t
o
tak
e
o
w
n
e
r
s
h
ip
o
f
th
eir
lear
n
i
n
g
an
d
b
ec
o
m
e
in
d
ep
en
d
en
t
p
r
o
b
lem
-
s
o
lv
er
s
.
Ultim
ately
,
d
ev
elo
p
th
e
r
esil
ien
cy
to
p
e
r
s
ev
er
e
th
r
o
u
g
h
ch
allen
g
es
in
m
ath
em
atics.
Ov
e
r
all,
a
SLE
an
d
T
S
c
r
ea
te
a
d
y
n
am
ic
p
ar
t
n
er
s
h
ip
b
etwe
en
s
tu
d
en
ts
an
d
teac
h
er
s
.
A
S
L
E
is
a
p
iv
o
tal
p
r
ed
icto
r
in
p
r
o
m
o
tin
g
s
tu
d
en
t
en
g
ag
em
e
n
t,
m
o
tiv
atio
n
,
a
n
d
o
v
er
all
ac
ad
e
m
ic
s
u
cc
ess
[
3
8
]
.
Stu
d
en
ts
f
ee
l
em
p
o
wer
ed
to
l
ea
r
n
,
ask
q
u
esti
o
n
s
,
an
d
tack
le
ch
allen
g
es.
T
h
is
in
tu
r
n
,
f
o
s
ter
s
a
p
o
s
itiv
e
attitu
d
e
to
war
d
s
m
ath
.
3
.
3
.
Da
t
a
inte
g
r
a
t
io
n
I
n
a
m
ix
ed
m
eth
o
d
s
s
tu
d
y
,
d
ata
in
teg
r
atio
n
is
an
im
p
o
r
t
an
t
asp
ec
t.
I
t
r
ef
er
s
to
th
e
m
eth
o
d
o
f
co
m
b
in
in
g
an
d
in
te
r
p
r
etin
g
th
e
q
u
an
titativ
e
r
esu
lts
an
d
q
u
alitativ
e
f
in
d
in
g
s
o
f
th
e
s
tu
d
y
by
C
r
eswell
[
39
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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20
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1
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Als
o
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wh
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i
)
p
a
r
ticip
an
t
-
d
r
iv
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in
teg
r
atio
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is
cr
u
cial
f
o
r
ca
p
tu
r
in
g
th
e
tar
g
et
g
r
o
u
p
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s
v
iewp
o
in
ts
;
ii
)
v
is
u
al
s
u
p
p
o
r
t
is
n
ec
ess
ar
y
to
lo
wer
l
an
g
u
ag
e
o
r
k
n
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wled
g
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b
ar
r
ier
s
;
an
d
iii
)
r
ea
l
-
tim
e
in
teg
r
atio
n
is
n
ec
ess
ar
y
f
o
r
q
u
ick
in
ter
p
r
etatio
n
.
T
h
e
p
r
ac
tic
al
im
p
ac
t o
f
r
esear
ch
in
r
ea
l
-
wo
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ld
s
ettin
g
s
ca
n
b
e
in
cr
ea
s
ed
b
y
u
s
in
g
th
is
ap
p
r
o
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ch
to
h
elp
p
r
ac
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o
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er
s
b
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u
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er
s
tan
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esear
ch
f
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d
in
g
s
,
ac
tiv
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p
ar
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d
ata
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p
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etatio
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as
it
is
g
ath
er
ed
,
a
n
d
u
s
e
th
ese
in
s
ig
h
t
s
to
g
u
id
e
th
eir
p
r
ac
tices
[
4
0
]
.
T
ab
le
3
s
h
o
ws
th
e
d
ata
in
teg
r
atio
n
o
f
th
is
s
eq
u
e
n
tial e
x
p
lan
ato
r
y
s
tu
d
y
.
T
ab
le
3
.
Data
in
teg
r
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n
To
p
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c
Q
u
a
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t
i
t
a
t
i
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d
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t
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u
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t
s m
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l
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e
n
c
e
(
r
=
0
.
1
4
1
,
p
=
0
.
0
0
5
)
R
2
:
“
U
n
d
e
r
s
t
a
n
d
,
f
o
c
u
s
,
t
r
y
,
a
n
d
s
o
l
v
e
.
O
f
c
o
u
r
s
e
,
i
f
y
o
u
u
n
d
e
r
s
t
a
n
d
t
h
e
p
r
o
b
l
e
m
,
y
o
u
k
n
o
w
w
h
a
t
f
o
rm
u
l
a
y
o
u
n
e
e
d
t
o
u
se.
Y
o
u
a
l
s
o
n
e
e
d
t
o
f
o
c
u
s..
.
T
h
e
n
I
t
ry
t
o
s
o
l
v
e
i
t
,
a
n
d
i
f
I
d
o
n
'
t
g
e
t
t
h
e
r
i
g
h
t
a
n
s
w
e
r,
I
t
r
y
a
g
a
i
n
u
si
n
g
n
e
w
t
h
i
n
g
s
o
r s
t
r
a
t
e
g
i
e
s
.
”
R
3
:
“
Fi
rs
t
,
I
re
c
a
l
l
w
h
a
t
S
i
r
S
e
a
n
t
a
u
g
h
t
u
s,
d
i
f
f
e
re
n
t
t
o
p
i
c
s,
a
n
d
t
h
e
n
I
c
re
a
t
e
m
y
o
w
n
q
u
e
st
i
o
n
s
t
h
a
t
a
re
m
o
r
e
d
i
f
f
i
c
u
l
t
t
o
s
e
e
i
f
I
c
a
n
a
n
sw
e
r t
h
e
m
o
r
n
o
t
.
”
R
-
4
:
“
Y
e
s,
s
i
r,
b
e
c
a
u
se
I
c
h
a
l
l
e
n
g
e
m
y
sel
f
t
o
i
m
p
r
o
v
e
a
t
h
o
m
e
,
s
i
r,
s
o
t
h
a
t
w
h
e
n
I
c
o
m
e
t
o
s
c
h
o
o
l
,
m
y
k
n
o
w
l
e
d
g
e
i
n
m
a
t
h
i
s
a
l
re
a
d
y
i
m
p
ro
v
e
d
.
”
R
-
1
:
“
Wi
t
h
t
h
e
h
e
l
p
o
f
p
ra
c
t
i
c
i
n
g
a
n
d
rev
i
e
w
i
n
g
t
h
e
t
o
p
i
c
r
e
p
e
a
t
e
d
l
y
,
I
c
a
n
e
v
e
n
t
u
a
l
l
y
u
n
d
e
r
st
a
n
d
i
t
.
.
.
.
l
e
a
rn
f
ro
m
m
y
m
i
st
a
k
e
s
i
n
t
h
i
s
s
p
e
c
i
f
i
c
t
o
p
i
c
a
n
d
re
v
i
e
w
a
n
d
l
e
a
r
n
a
g
a
i
n
f
o
r
t
h
e
n
e
x
t
q
u
i
z
so
t
h
a
t
I
c
a
n
g
e
t
a
h
i
g
h
e
r
sc
o
r
e
a
n
d
i
m
p
ro
v
e
m
y
p
e
r
f
o
rm
a
n
c
e
.
”
G
r
o
w
t
h
mi
n
d
se
t
i
n
f
l
u
e
n
c
e
d
m
a
t
h
r
e
si
l
i
e
n
c
e
(
r
=
0
.
0
7
7
,
p
=
0
.
0
3
3
)
R
e
s
3
:
“
A
c
t
u
a
l
l
y
,
s
o
m
e
t
i
m
e
s
I
g
e
t
e
x
c
i
t
e
d
a
n
d
c
o
n
f
i
d
e
n
t
s
o
l
v
i
n
g
t
h
e
s
e
p
r
o
b
l
e
m
s
.
L
i
k
e
r
i
g
h
t
n
o
w
,
w
i
t
h
w
h
a
t
S
i
r
S
e
a
n
t
a
u
g
h
t
u
s
a
b
o
u
t
p
r
o
b
a
b
i
l
i
t
y
,
w
e
a
l
r
e
a
d
y
l
e
a
r
n
e
d
s
o
m
e
o
f
i
t
i
n
G
r
a
d
e
1
0
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o
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f
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m
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r
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o
n
f
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d
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t
s
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n
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t
e
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n
t
h
o
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g
h
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t
'
s
m
o
r
e
d
i
f
f
i
c
u
l
t
n
o
w
.
”
R
e
s
5
:
“
Y
e
s,
si
r.
Be
c
a
u
se
y
o
u
c
a
n
l
e
a
r
n
f
r
o
m
d
o
i
n
g
i
t
.
S
o
,
b
y
j
u
st
t
ry
i
n
g
,
I
t
h
i
n
k
I
c
a
n
f
i
g
u
r
e
i
t
o
u
t
.
S
o
,
i
t
'
s
n
o
t
a
p
ro
b
l
e
m
f
o
r
m
e
t
o
f
a
c
e
n
e
w
p
r
o
b
l
e
m
s
.
”
R
e
s
6
:
“
Y
e
a
h
,
b
e
c
a
u
se
I
t
h
i
n
k
I
c
a
n
d
o
i
t
.
I
'
l
l
p
u
sh
m
y
s
e
l
f
h
a
r
d
e
r
t
o
s
o
l
v
e
i
t
b
e
c
a
u
s
e
I
'
m
a
f
a
st
l
e
a
r
n
e
r
a
n
d
I
f
i
n
d
m
a
t
h
i
n
t
e
rest
i
n
g
,
so
I
w
i
l
l
d
e
f
i
n
i
t
e
l
y
s
o
l
v
e
i
t
.
”
Te
a
c
h
e
r
sc
a
f
f
o
l
d
i
n
g
i
n
f
l
u
e
n
c
e
d
m
a
t
h
e
m
a
t
i
c
s
r
e
si
l
i
e
n
c
e
(
r
=
0
.
1
0
7
,
p
=
0
.
0
3
5
)
R
e
s
p
1
:
“
H
e
p
r
o
v
i
d
e
s
a
f
i
l
e
w
i
t
h
c
o
n
t
e
n
t
r
e
l
a
t
e
d
t
o
t
h
e
t
o
p
i
c
,
a
n
d
t
h
e
i
n
f
o
rm
a
t
i
o
n
t
h
e
re
i
s c
l
e
a
rer
.
”
R
e
s
p
3
(
f
i
r
st
p
a
r
t
)
:
“
U
h
m
,
l
i
k
e
t
h
e
g
u
i
d
e
s
S
i
r
s
e
n
d
s
u
s
o
n
h
o
w
t
o
so
l
v
e
a
p
a
r
t
i
c
u
l
a
r
q
u
e
st
i
o
n
.
”
R
e
s
p
5
:
“
S
o
m
e
t
i
m
e
s
h
e
'
l
l
g
i
v
e
u
s
a
Y
o
u
T
u
b
e
so
u
rc
e
t
o
u
n
d
e
rs
t
a
n
d
t
h
e
c
o
n
c
e
p
t
c
l
e
a
rl
y
o
r
t
h
e
e
a
s
i
e
st
w
a
y
t
o
f
i
g
u
re
i
t
o
u
t
.
S
o
m
e
t
i
m
e
s,
h
e
e
x
p
l
a
i
n
s
i
t
h
i
m
se
l
f
.
”
R
e
s
p
6
:
“
T
h
i
s
s
e
m
e
s
t
e
r,
y
e
s
,
h
e
se
n
d
s
i
m
a
g
e
s
w
i
t
h
f
o
rm
u
l
a
s
o
n
h
o
w
t
o
so
l
v
e
p
ro
b
l
e
m
s
a
n
d
e
x
p
l
a
i
n
s
w
h
a
t
t
h
e
t
o
p
i
c
i
s
a
b
o
u
t
.
”
PSS
an
d
m
ath
r
esil
ien
ce
.
I
t c
a
n
b
e
g
lean
ed
f
r
o
m
th
e
tab
le
th
at
PS
S
p
r
ed
icts
m
ath
r
esil
ien
ce
(
r
=0
.
1
4
1
,
p
=0
.
0
0
5
)
.
th
is
r
esu
lt
was
ex
p
lain
ed
b
y
th
e
q
u
alitativ
e
d
ata
h
ig
h
lig
h
tin
g
th
e
asp
ec
ts
o
f
PSS
an
d
th
ei
r
co
n
n
ec
tio
n
to
m
at
h
r
esil
ien
ce
.
I
t sh
o
ws a
p
r
o
ce
s
s
-
or
ien
ted
ap
p
r
o
ac
h
.
W
h
ile
th
e
s
tatem
en
ts
f
r
o
m
I
2
,
I
3
,
I
1
(
last
s
en
ten
ce
)
s
h
o
wca
s
e
th
e
im
p
o
r
tan
ce
o
f
tr
y
in
g
d
i
f
f
er
en
t
a
p
p
r
o
ac
h
es,
lear
n
in
g
f
r
o
m
m
i
s
tak
es,
an
d
ac
tiv
ely
p
r
ac
ticin
g
to
im
p
r
o
v
e
PSS
.
T
h
is
p
er
s
ev
er
an
ce
in
t
h
e
f
ac
e
o
f
ch
allen
g
es
is
a
k
ey
asp
ec
t
o
f
r
es
ilien
ce
.
Mo
r
eo
v
er
,
cr
ea
ti
n
g
c
h
allen
g
in
g
p
r
o
b
lem
s
f
o
r
th
em
s
elv
es
(
I
3
)
an
d
ac
tiv
ely
s
ee
k
in
g
way
s
to
im
p
r
o
v
e
at
h
o
m
e
(
I
4
)
d
em
o
n
s
tr
ate
a
GM
an
d
a
p
r
o
ac
tiv
e
ap
p
r
o
ac
h
to
lear
n
in
g
,
lead
in
g
to
g
r
ea
ter
r
esil
ien
ce
.
As
a
wh
o
le,
th
e
s
tatem
en
ts
ex
p
lain
an
d
em
p
h
asize
th
at
u
n
d
er
s
tan
d
i
n
g
,
a
p
p
ly
in
g
s
tr
ateg
ies,
p
er
s
is
ten
ce
,
s
elf
-
ch
allen
g
e,
an
d
a
GM
p
r
o
v
id
e
th
e
s
tr
o
n
g
est
ju
s
tific
atio
n
f
o
r
th
e
q
u
an
titat
iv
e
r
esu
lt
th
at
PS
S
in
f
lu
en
ce
m
ath
e
m
atics
r
esil
i
en
ce
.
Fu
r
th
er
m
o
r
e,
t
h
e
r
esu
lt
is
co
n
f
ir
m
ed
in
t
h
e
r
ese
ar
ch
co
n
d
u
cted
b
y
C
o
u
s
i
n
s
et
a
l.
[
2
4
]
th
at
s
tu
d
en
ts
o
v
er
ca
m
e
th
ei
r
em
o
tio
n
al
b
ar
r
ier
s
to
lear
n
i
n
g
m
ath
em
atic
s
s
u
p
p
o
r
t
f
r
o
m
an
y
f
ac
to
r
s
,
th
er
e
a
r
e
s
en
s
itiv
e
s
u
p
p
o
r
t
f
r
o
m
o
th
er
s
,
s
p
ec
if
ic
teac
h
in
g
an
d
lear
n
in
g
s
tr
ateg
ies,
a
n
d
in
cr
ea
s
in
g
th
eir
m
ath
em
atica
l
r
esil
ien
ce
.
I
n
ad
d
itio
n
,
s
tu
d
en
ts
with
s
tr
o
n
g
m
ath
em
atica
l
r
esil
ien
ce
,
h
av
e
a
d
ap
tiv
e
attitu
d
es
o
r
ca
n
ad
a
p
t
to
th
e
e
n
v
ir
o
n
m
en
t
;
ca
n
f
ac
e
u
n
ce
r
tain
ty
an
d
ch
allen
g
e
p
r
o
b
lem
s
;
s
o
lv
e
p
r
o
b
l
em
s
lo
g
ically
a
n
d
f
lex
ib
ly
;
lo
o
k
f
o
r
cr
ea
tiv
e
s
o
l
u
tio
n
s
to
ch
allen
g
es;
ar
e
cu
r
i
o
u
s
an
d
lear
n
f
r
o
m
ex
p
e
r
ien
c
e;
h
av
e
s
elf
-
co
n
tr
o
l
ab
ilit
y
; a
war
e
o
f
h
is
f
ee
lin
g
s
; h
as a
s
tr
o
n
g
an
d
ea
s
y
s
o
cial
n
e
two
r
k
[
4
1
].
GM
an
d
m
ath
r
esil
ien
ce
,
t
h
e
r
esu
lt
s
h
o
wed
th
at
GM
p
r
ed
i
cts
m
ath
r
esil
ien
ce
(
r
=0
.
0
7
7
,
p
=0
.
0
3
3
)
.
T
h
e
r
esu
lt
was
ex
p
lain
ed
b
y
t
h
e
s
tatem
en
t
o
f
I
3
wh
ich
d
em
o
n
s
tr
ates
a
GM
b
ec
au
s
e
th
e
s
t
u
d
en
t
co
n
n
ec
ts
p
r
io
r
k
n
o
wled
g
e
to
b
u
ild
co
n
f
id
e
n
ce
in
tack
lin
g
a
m
o
r
e
ch
a
llen
g
in
g
p
r
o
b
lem
.
T
h
e
y
v
ie
w
d
if
f
icu
lty
as
an
o
p
p
o
r
tu
n
ity
to
g
r
o
w
th
eir
a
b
ilit
ies.
Als
o
,
I
5
em
p
h
as
izes
a
k
ey
asp
ec
t
o
f
a
GM
-
th
e
b
elief
th
at
in
tellig
en
ce
an
d
ab
ilit
ies
ca
n
b
e
d
ev
elo
p
ed
th
r
o
u
g
h
ef
f
o
r
t
a
n
d
lear
n
in
g
.
T
h
e
y
ap
p
r
o
ac
h
n
ew
p
r
o
b
lem
s
wit
h
th
e
co
n
f
id
en
ce
th
at
th
ey
ca
n
f
ig
u
r
e
th
em
o
u
t
th
r
o
u
g
h
tr
y
in
g
.
I
n
ad
d
itio
n
,
I
6
s
h
o
wca
s
es
a
G
M
b
y
d
em
o
n
s
tr
atin
g
a
b
elief
in
th
eir
ab
ilit
y
to
lear
n
an
d
a
willin
g
n
ess
to
p
u
s
h
th
em
s
elv
es.
T
h
ey
f
in
d
m
ath
in
ter
esti
n
g
an
d
s
ee
ch
allen
g
es
as
o
p
p
o
r
tu
n
ities
to
lear
n
an
d
i
m
p
r
o
v
e
.
I
n
s
u
m
m
ar
y
,
s
tatem
en
ts
f
r
o
m
I
3
,
I
5
,
an
d
I
6
d
e
m
o
n
s
tr
ate
a
GM
b
y
h
ig
h
lig
h
tin
g
th
e
b
elief
in
th
eir
ab
ilit
y
to
lear
n
,
im
p
r
o
v
e,
a
n
d
tack
le
ch
allen
g
es,
wh
ich
co
n
tr
ib
u
tes
to
m
ath
r
esil
ien
cy
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
B
ey
o
n
d
th
e
s
co
r
e:
a
s
eq
u
e
n
tia
l stu
d
y
o
n
th
e
p
r
ed
icto
r
s
o
f stu
d
en
t res
ilien
ce
in
…
(
R
o
a
r
A
.
C
a
lla
ma
n
)
1385
T
h
e
r
esu
lt
is
co
n
f
ir
m
ed
b
y
Pa
u
n
esk
u
et
a
l.
[4
2
]
t
h
at
GM
p
lay
a
cr
u
cial
r
o
le
in
d
ev
elo
p
in
g
r
esil
ien
ce
,
esp
ec
ially
am
o
n
g
d
is
ad
v
an
ta
g
ed
s
tu
d
en
ts
wh
o
f
r
e
q
u
en
tly
f
a
ce
ac
ad
em
ic
s
etb
ac
k
s
.
I
n
a
d
d
i
tio
n
,
h
o
ld
in
g
a
GM
in
cr
ea
s
es
an
in
d
iv
id
u
al
’
s
r
esil
ien
ce
,
p
er
s
ev
er
an
ce
,
an
d
attitu
d
es
to
war
d
lear
n
in
g
[
4
3
]
,
[
4
4
]
.
Stu
d
en
ts
with
a
GM
ar
e
m
o
r
e
lik
ely
to
p
er
ce
iv
e
ac
ad
em
ic
ch
allen
g
es
as
o
p
p
o
r
tu
n
ities
to
im
p
r
o
v
e
th
eir
ab
ilit
y
an
d
lear
n
in
g
sk
ills
,
an
d
th
er
ef
o
r
e
,
th
ey
e
x
h
i
b
it h
ig
h
er
le
v
els o
f
r
esil
ien
ce
[
4
5
]
,
[
4
6
].
T
S
an
d
m
ath
r
esil
ien
ce
.
I
t
c
an
b
e
n
o
te
d
th
at
q
u
a
n
titativ
e
f
in
d
in
g
s
r
ev
ea
le
d
T
S
in
f
lu
e
n
ce
d
m
ath
r
esil
ien
ce
(
r
-
0
.
1
0
7
,
p
=
0
.
0
3
5
)
.
T
h
is
r
esu
lt
was
e
x
p
lain
ed
b
y
th
e
q
u
alitativ
e
d
ata
wh
i
ch
h
ig
h
lig
h
ted
th
e
im
p
o
r
tan
ce
o
f
p
r
o
v
id
in
g
ad
d
i
tio
n
al
r
eso
u
r
ce
s
,
clea
r
in
s
tr
u
c
tio
n
s
,
an
d
d
if
f
er
en
tiated
in
s
tr
u
ctio
n
s
.
I
n
ess
en
ce
,
s
u
p
p
ly
in
g
clea
r
an
d
co
n
cise
g
u
id
es
(
I
1
,
I
3
,
I
5
,
a
n
d
I
6
)
o
r
e
x
p
lan
atio
n
s
tailo
r
ed
t
o
s
tu
d
en
t
n
ee
d
s
h
elp
s
b
r
i
d
g
e
u
n
d
er
s
tan
d
i
n
g
g
ap
s
an
d
em
p
o
wer
s
s
tu
d
en
ts
to
ap
p
r
o
ac
h
p
r
o
b
lem
s
in
d
ep
en
d
e
n
tly
.
T
h
i
s
f
o
s
ter
s
a
s
en
s
e
o
f
s
elf
-
ef
f
icac
y
.
Of
f
er
in
g
r
eso
u
r
c
es
lik
e
v
id
e
o
s
o
r
alter
n
ativ
e
e
x
p
lan
atio
n
s
(
I
5
)
ca
ter
s
to
d
if
f
e
r
en
t
lear
n
i
n
g
s
ty
les
an
d
en
s
u
r
es a
ll st
u
d
en
ts
h
a
v
e
t
h
e
o
p
p
o
r
tu
n
ity
to
g
r
asp
co
n
ce
p
ts
ef
f
ec
tiv
ely
.
Ov
er
all,
th
e
s
tatem
en
ts
th
at
em
p
h
asize
p
r
o
v
id
in
g
clea
r
ex
p
lan
atio
n
s
,
ad
d
itio
n
al
r
eso
u
r
ce
s
,
an
d
d
if
f
er
en
tiated
in
s
tr
u
ctio
n
p
r
o
v
id
e
th
e
s
tr
o
n
g
est
ju
s
tific
atio
n
f
o
r
th
e
r
esu
lt
th
at
T
S
p
r
e
d
ic
ts
m
ath
r
esil
ien
ce
.
T
h
e
r
esu
lt
is
s
u
p
p
o
r
te
d
b
y
K
h
u
m
alo
et
a
l.
[4
7
]
s
tated
th
at
t
ea
ch
er
s
u
p
p
o
r
t,
en
c
o
u
r
a
g
em
e
n
t,
an
d
i
n
s
tr
u
ctio
n
al
s
tr
ateg
ies
co
n
tr
ib
u
te
to
s
tu
d
e
n
ts
’
r
esil
ien
ce
in
tack
lin
g
m
ath
em
atica
l
ch
allen
g
es.
I
n
a
d
d
itio
n
,
th
e
m
eta
-
an
aly
s
is
s
tu
d
y
o
f
Veld
h
u
is
[
4
8
]
teac
h
er
s
’
tr
ain
in
g
in
in
s
tr
u
ctio
n
al
ap
p
r
o
ac
h
es
f
o
s
ter
r
esil
ien
ce
,
s
u
ch
as
s
ca
f
f
o
ld
in
g
a
n
d
f
o
r
m
ativ
e
ass
ess
m
en
t,
p
o
s
itiv
ely
im
p
ac
t stu
d
en
ts
’
m
ath
em
atica
l
r
esil
ien
ce
.
4.
CO
NCLU
SI
O
N
B
ased
o
n
th
e
f
in
d
in
g
s
,
it
is
co
n
clu
d
ed
t
h
at
th
e
co
g
n
itiv
e
(
PS
S
)
,
p
s
y
ch
o
lo
g
ical
(
GM
)
,
a
n
d
s
o
cial
(
TS
)
f
ac
to
r
s
s
ig
n
if
ican
tly
in
f
lu
en
ce
d
s
tu
d
en
ts
’
m
ath
em
atics
r
esil
i
en
cy
in
p
r
o
b
lem
-
s
o
lv
in
g
.
Fu
r
t
h
er
,
m
ath
r
esil
ien
ce
is
f
o
s
ter
ed
b
y
a
GM
,
a
s
u
p
p
o
r
tiv
e
en
v
ir
o
n
m
en
t,
an
d
TS
.
T
h
u
s
,
v
alid
ated
p
r
o
p
o
s
itio
n
2
wh
ich
s
tates
th
at
co
g
n
itiv
e,
p
s
y
ch
o
lo
g
ical,
an
d
s
o
cial
f
ac
to
r
s
ar
e
in
f
lu
en
tial
t
o
a
s
tu
d
en
ts
’
r
esil
ien
ce
in
s
o
l
v
in
g
m
ath
em
atica
l
p
r
o
b
lem
s
.
R
esear
ch
m
ay
b
e
e
x
p
ec
ted
to
in
clu
d
e
STE
M
-
tr
ac
k
s
tu
d
en
ts
o
r
s
tu
d
en
ts
f
r
o
m
d
i
f
f
er
en
t
g
r
a
d
e
lev
els
to
d
eter
m
in
e
if
th
e
p
r
ed
icto
r
s
o
f
r
esil
ien
ce
v
ar
y
s
ig
n
if
ican
tly
ac
r
o
s
s
ac
ad
em
ic
b
ac
k
g
r
o
u
n
d
s
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
e
au
th
o
r
s
s
tate
n
o
f
u
n
d
in
g
in
v
o
lv
e
d
o
n
t
h
is
s
tu
d
y
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
t
r
ib
u
to
r
R
o
les
T
a
x
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
i
d
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Na
m
e
o
f
Aut
ho
rs
C
M
So
Va
Fo
I
R
D
O
E
Vi
Su
P
Fu
R
o
ar
A.
C
allam
a
n
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Am
elia
M.
B
o
n
o
tan
✓
✓
✓
✓
✓
✓
✓
✓
C
:
C
o
n
c
e
p
t
u
a
l
i
z
a
t
i
o
n
M
:
M
e
t
h
o
d
o
l
o
g
y
So
:
So
f
t
w
a
r
e
Va
:
Va
l
i
d
a
t
i
o
n
Fo
:
Fo
r
mal
a
n
a
l
y
s
i
s
I
:
I
n
v
e
s
t
i
g
a
t
i
o
n
R
:
R
e
so
u
r
c
e
s
D
:
D
a
t
a
C
u
r
a
t
i
o
n
O
:
W
r
i
t
i
n
g
-
O
r
i
g
i
n
a
l
D
r
a
f
t
E
:
W
r
i
t
i
n
g
-
R
e
v
i
e
w
&
E
d
i
t
i
n
g
Vi
:
Vi
su
a
l
i
z
a
t
i
o
n
Su
:
Su
p
e
r
v
i
s
i
o
n
P
:
P
r
o
j
e
c
t
a
d
mi
n
i
st
r
a
t
i
o
n
Fu
:
Fu
n
d
i
n
g
a
c
q
u
i
si
t
i
o
n
CO
NF
L
I
C
T
O
F
I
N
T
E
R
E
S
T
ST
A
T
E
M
E
NT
T
h
e
au
th
o
r
d
ec
lar
es n
o
co
n
f
lict o
f
in
ter
est.
DATA AV
AI
L
AB
I
L
I
T
Y
Der
iv
ed
d
ata
s
u
p
p
o
r
ti
n
g
th
e
f
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